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Astashkin, S., Lesnik, K. & Maligranda, L. (2019). Isomorphic structure of Cesàro and Tandori spaces. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 71(3), 501-532
Open this publication in new window or tab >>Isomorphic structure of Cesàro and Tandori spaces
2019 (English)In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-2479, Vol. 71, no 3, p. 501-532Article in journal (Refereed) Published
Abstract [en]

We investigate the isomorphic structure of the Cesàro spaces and their duals, the Tandori spaces. The main result states that the Cesàro function space Ces∞ and its sequence counterpart ces∞ are isomorphic. This is rather surprising since Ces∞ (like Talagrand’s example) has no natural lattice predual. We prove that ces∞ is not isomorphic to ℓ∞ nor is Ces∞ isomorphic to the Tandori space L1 with the norm ∥f∥L1 = ∥f∥L1, where f(t) = esssups≥tf(s). Our investigation also involves an examination of the Schur and Dunford–Pettis properties of Cesàro and Tandori spaces. In particular, using results of Bourgain we show that a wide class of Cesàro–Marcinkiewicz and Cesàro–Lorentz spaces have the latter property.

Place, publisher, year, edition, pages
Cambridge University Press, 2019
Keywords
Cesàro and Tandori sequence spaces, Cesàro and Tandori function spaces, Cesàro operator, Banach ideal space, symmetric space, Schur property, Dunford–Pettis property, isomorphism
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-74679 (URN)10.4153/CJM-2017-055-8 (DOI)000468458800001 ()2-s2.0-85066078576 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-06-18 (johcin)

Available from: 2019-06-18 Created: 2019-06-18 Last updated: 2019-06-18Bibliographically approved
Jóźwik, I., Maligranda, L. & Terepeta, M. (2019). Stefan Kempisty (1892-1940). Historia Mathematica, 48, 69-86
Open this publication in new window or tab >>Stefan Kempisty (1892-1940)
2019 (English)In: Historia Mathematica, ISSN 0315-0860, E-ISSN 1090-249X, Vol. 48, p. 69-86Article in journal (Refereed) Published
Abstract [en]

Stefan Kempisty was a Polish mathematician, working on the theory of real functions, set theory, integrals, interval functions and the theory of surface area. In 1919 he defended his Ph.D. thesis, On semi-continuous functions, at the Jagiellonian University in Cracow under the supervision of Kazimierz Żorawski. In December 1924 he did his habilitation at the University of Warsaw and continued his work at the Stefan Batory University in Vilnius. Kempisty published over forty scientific papers, three textbooks and one monograph. Kempisty's name in mathematics appears in connection with the definition of quasi-continuous functions, different kinds of continuity of functions of several variables, the classification of Baire, Young and Sierpiński functions, interval functions, and Denjoy or Burkill integrals.

This paper is prepared for a wide range of readers. It is an abridged version of the article written in Polish by the same authors (cf. Jóźwik et al., 2017), where can be found more detailed information.

Abstract [pl]

Stefan Kempisty był polskim matematykiem zajmującym się funkcjami zmiennej rzeczywistej, teorią mnogości, całkami, funkcjami przedziału i teorią pola powierzchni. W 1919 roku obronił pracę doktorską O funkcjach nawpółciągłych na Uniwersytecie Jagiellońskim w Krakowie, a jego promotorem był Kazimierz Żorawski. W grudniu 1924 roku habilitował się na Uniwersytecie Warszawskim. W latach 1920–1939 pracował na Uniwersytecie Stefana Batorego w Wilnie. Opublikował ponad czterdzieści prac naukowych i trzy podręczniki z analizy rzeczywistej oraz jedną monografię. Reprezentował w swoich pracach i na seminariach szkołę warszawską. Nazwisko Kempistego w matematyce pojawia się w związku z definicją funkcji quasi-ciągłej, różnymi ciągłościami funkcji wielu zmiennych, klasyfikacją funkcji Baire'a, Younga i Sierpińskiego, funkcjami przedziału oraz całkami Denjoy i Burkilla.

Praca ta jest skróconą wersją artykułu napisanego po polsku przez tych samych autorów (cf. Jóźwik et al., 2017), w której można znaleźć bardziej szczegółowe informacje.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
20th century mathematics and mathematicians in Europe, Stefan Kempisty, Kempisty's integral, Quasi-continuous functions, Interval functions, Surface area
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-73153 (URN)10.1016/j.hm.2019.01.003 (DOI)000484652300003 ()
Available from: 2019-03-11 Created: 2019-03-11 Last updated: 2019-10-01Bibliographically approved
Kolwicz, P., Leśnik, K. & Maligranda, L. (2019). Symmetrization, factorization and arithmetic of quasi-Banach function spaces. Journal of Mathematical Analysis and Applications, 470(2), 1136-1166
Open this publication in new window or tab >>Symmetrization, factorization and arithmetic of quasi-Banach function spaces
2019 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 470, no 2, p. 1136-1166Article in journal (Refereed) Published
Abstract [en]

We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderón–Lozanovskiĭ spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the symmetrization commutates with these operations. We determine also the spaces of pointwise multipliers between Lorentz spaces and Cesàro spaces. The methods that we develop may be regarded as an arithmetic of quasi-Banach function spaces and proofs of Theorem 3, Theorem 4, Theorem 6 give a kind of tutorial for these methods. Finally, the above results will be used in proofs of some factorization results.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Quasi-Banach ideal spaces, Symmetrization operation, Calderón–Lozanovskiĭ spaces, Symmetric spaces, Pointwise products and multipliers, Cesàro spaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-71318 (URN)10.1016/j.jmaa.2018.10.054 (DOI)000450543200026 ()2-s2.0-85055099280 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-11-07 (johcin) 

Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2019-01-10Bibliographically approved
Maligranda, L. & Strelcyn, J. (2018). Jan Ptaszycki (1854-1912). Antiquitates Mathematicae, 12(1), 31-80
Open this publication in new window or tab >>Jan Ptaszycki (1854-1912)
2018 (Polish)In: Antiquitates Mathematicae, ISSN 1898-5203, E-ISSN 2353-8813, Vol. 12, no 1, p. 31-80Article in journal (Refereed) Published
Abstract [pl]

Jan Ptaszycki był polskim matematykiem pracującym w Petersburgu w latach 1876-1912. W Polsce jest zapomniany, a w Rosji uważany zazwyczaj za rosyjskiego matematyka, znanego tam jako Iwan Lwowicz Ptaszycki. W rosyjskiej literaturze historyczno-matematycznej, w zależności od autora, podaje się, że Ptaszycki był rosyjskim matematykiem lub, rzadziej, polskim matematykiem, na przykład u Łokoć (2015, 2018). Ważne informacje o Ptaszyckim pochodzą z nekrologów K. A. Posse (1912) i S. Dicksteina (1912) oraz ze wspomnień I. Ja. Depmana (1960), którzy znali go osobiście. Chcemy przybliżyć współczesnemu czytelnikowi tego zapomnianego polskiego matematyka pracującego w Petersburgu. Po omówieniu jego biografii krótko omawiamy jego prace matematyczne. Na zakończenie artykułu cytujemy artykuły i książki związane z dorobkiem naukowym Ptaszyckiego oraz podajemy pełną listę prac i ksiązek, które opublikował a także listę prac, gdzie można znaleźć informacje o nim.

Abstract [en]

Jan Ptaszycki was a Polish mathematician working in St. Petersburg in the period 1876–1912. In Poland, he is forgotten, and in Russia considered generally as a Russian mathematician, known there as Ivan Lvovich Ptaszycki. In Russian literature about history of mathematics, depending on the author, it is reported that Ptaszycki was a Russian mathematician or, more rarely, a Polish mathematician as, for example, in Lokot (2015, 2018). The important information about Ptaszycki comes from the obituaries of K. A. Posse (1912) and S. Dickstein (1912) and from the memoirs of I. Ja. Depman (1960), that is from people who knew him personally. We wanted to make known to the contemporary reader this forgotten Polish mathematician working in St. Petersburg. This article tries to reach his work and achievement in mathematics as well as information about his activity. After discussing his biography, we briefly discuss his mathematical work. At the end of this paper, we quote articles and books related to Ptaszycki scientific achievements and we present a full list of his published works and books, and also references where one can find information about him.

Place, publisher, year, edition, pages
Warszawa: Polskie Towarzystwo Matematyczne, 2018
Keywords
Jan Ptaszycki, biographies, St. Petersburg University, history of mathematics in Russia, integration in finite form, differential algebra, Jan Ptaszycki, biografie, Uniwersytet Petersburski, historia matematyki w Rosji, całkowanie w postaci skończonej, algebra różniczkowa
National Category
Natural Sciences Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-73519 (URN)10.14708/am.v12i1.6406 (DOI)
Note

Validerad;2019;Nivå 1;2019-08-20 (johcin)

Available from: 2019-04-08 Created: 2019-04-08 Last updated: 2019-08-20Bibliographically approved
Maligranda, L. (2018). Lech Maligranda: laureat Nagrody Głównej PTM im. Samuela Dicksteina za 2016 rok. Antiquitates Mathematicae, 12(1), 285-297
Open this publication in new window or tab >>Lech Maligranda: laureat Nagrody Głównej PTM im. Samuela Dicksteina za 2016 rok
2018 (Polish)In: Antiquitates Mathematicae, ISSN 1898-5203, E-ISSN 2353-8813, Vol. 12, no 1, p. 285-297Article in journal, Editorial material (Other academic) Published
Abstract [pl]

Nagroda im. Samuela Dicksteina jest przyznawana za wybitne osiągniecia w dziedzinie edukacji matematycznej, popularyzacji i historii matematyki. Została ustanowiona w 1978 roku a pierwszym, który ją otrzymał był Stefan Straszewicz. W 2016 roku nagroda główną PTM im. Samuela Dicksteina został uhonorowany professor Lech Maligranda z Uniwersytetu Technicznego w Luleå (Szwecja) za wybitne osiągniecia w dziedzinie historii matematyki.

Abstract [en]

The Samuel Dickstein’s prize is awarded for outstanding achievements in the field of mathematical education, popularization and history of mathematics. It was established in 1978 and the first one recognized by it was Stefan Straszewicz. In 2016, the Samuel Dicstein main PTM award was honored with Professor Lech Maligranda from the Technical University of Luleå (Sweden) for outstanding achievements in the history of mathematics.

Place, publisher, year, edition, pages
Warszawa: Polskie Towarzystwo Matematyczne, 2018
Keywords
Dickstein prize, Polish Mathematical Society, Samuel Dickstein, edukacja matematyczna, popularyzacja matematyki
National Category
Natural Sciences Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-73522 (URN)10.14708/am.v12i0.6406 (DOI)
Available from: 2019-04-08 Created: 2019-04-08 Last updated: 2019-04-16Bibliographically approved
Astashkin, S. V. & Maligranda, L. (2018). Lp + L∞ and Lp n L∞ are not Isomorphic for all 1 ≤ p < ∞, p ≠ 2. Proceedings of the American Mathematical Society, 146(5), 2181-2194
Open this publication in new window or tab >>Lp + L and Lp n L are not Isomorphic for all 1 ≤ p < ∞, p ≠ 2
2018 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, no 5, p. 2181-2194Article in journal (Refereed) Published
Abstract [en]

We prove the result stated in the title. It comes as a consequence of the fact that the space Lp n L∞, 1 = p < ∞, p ≠ 2, does not contain a complemented subspace isomorphic to Lp. In particular, as a subproduct, we show that Lp nL∞ contains a complemented subspace isomorphic to l2 if and only if p = 2.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2018
Keywords
Symmetric spaces, isomorphic spaces, complemented subspaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-67826 (URN)10.1090/proc/13928 (DOI)000425993100030 ()2-s2.0-85046626311 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-03-02 (rokbeg)

Available from: 2018-03-02 Created: 2018-03-02 Last updated: 2019-06-19Bibliographically approved
Astashkin, S. V. & Maligranda, L. (2018). Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q. Comptes rendus. Mathematique, 356(6), 661-665
Open this publication in new window or tab >>Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
2018 (English)In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 356, no 6, p. 661-665Article in journal (Refereed) Published
Abstract [en]

We prove that if 1≤p,q≤∞1≤p,q≤∞, then the spaces Lp+LqLp+Lq and Lp∩LqLp∩Lq are isomorphic if and only if p=qp=q. In particular, L2+LL2+L∞ and L2∩LL2∩L∞ are not isomorphic, which is an answer to a question formulated in [2].

Abstract [fr]

Nous prouvons que si 1≤p,q≤∞1≤p,q≤∞, alors les espaces Lp+LqLp+Lq et Lp∩LqLp∩Lq sont isomorphes si et seulement si p=qp=q. En particulier, L2+LL2+L∞ et L2∩LL2∩L∞ ne sont pas isomorphes, ce qui est une réponse à une question formulée dans [2].

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Symmetric spaces, isomorphic spaces, complemented subspaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-68570 (URN)10.1016/j.crma.2018.04.019 (DOI)000433239800012 ()2-s2.0-85046360251 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-06-11 (rokbeg);

French title: [Lp + Lq et Lp ∩ Lq ne sont pas isomorphes pour tout 1 ≤ p,q ≤ ∞, p ≠ q]

Available from: 2018-05-02 Created: 2018-05-02 Last updated: 2019-06-19Bibliographically approved
Berezhnoǐ, E. I. & Maligranda, L. (2018). Represensibility of cones of monotone functions in weighted Lebesgue spaces and extrapolation of operators on these cones. St. Petersburg Mathematical Journal, 29(4), 545-574
Open this publication in new window or tab >>Represensibility of cones of monotone functions in weighted Lebesgue spaces and extrapolation of operators on these cones
2018 (English)In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 29, no 4, p. 545-574Article in journal (Refereed) Published
Abstract [en]

It is shown that a sublinear operator is bounded on the cone of monotone functions if and only if a certain new operator related to the one mentioned above is bounded on a certain ideal space defined constructively. This construction is used to provide new extrapolation theorems for operators on the cone in weighted Lebesgue spaces.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2018
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69491 (URN)10.1090/spmj/1506 (DOI)000434347800001 ()2-s2.0-85048032506 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-06-14 (andbra)

Available from: 2018-06-14 Created: 2018-06-14 Last updated: 2018-06-28Bibliographically approved
Maligranda, L. (2018). Review of the book by Mariusz Urbanek ``Genialni - Lwowska Szkoła Matematyczna" (Polish) [Geniuses - the Lvov school of mathematics] [Review]. Matematychni Studii, 50(1), 105-112
Open this publication in new window or tab >>Review of the book by Mariusz Urbanek ``Genialni - Lwowska Szkoła Matematyczna" (Polish) [Geniuses - the Lvov school of mathematics]
2018 (English)In: Matematychni Studii, ISSN 0094-1492, Vol. 50, no 1, p. 105-112Article, book review (Refereed) Published
Abstract [en]

This review is an extended version of my short review of Urbanek's book that was published in MathSciNet. Here it is written about his book in greater detail, which was not possible in the short review. I will present facts described in the book as well as some false information there.

Place, publisher, year, edition, pages
Lvov: , 2018
Keywords
Lvov School of Mathematics, functional analysis, Banach spaces
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-73520 (URN)10.15330/ms.50.1.105-112 (DOI)
Available from: 2019-04-08 Created: 2019-04-08 Last updated: 2019-04-15Bibliographically approved
Maligranda, L. & Prytula, J. (2018). Uniwersytet we Lwowie w latach 1939-1941: Nieopublikowane prace matematyków, fizyków i astronomów. Wiadomosci Matematyczne, 54(1), 67-78
Open this publication in new window or tab >>Uniwersytet we Lwowie w latach 1939-1941: Nieopublikowane prace matematyków, fizyków i astronomów
2018 (Polish)In: Wiadomosci Matematyczne, ISSN 2080-5519, Vol. 54, no 1, p. 67-78Article in journal (Refereed) Published
Abstract [pl]

Przedstawiono zawartość lwowskiego czasopisma Komunikaty Wydzialu Matematyczno-Fizycznego z lat 1940 i 1941, które znaleziono w archiwum. Wśród autorów byli: Stefan Banach, Leon Chwistek, Meier Eidelheit, Gertwagen, Jan Hercberg, Marian Mojżesz Jacob, Salomon Lubelski, Jan Mergentaler, Wasyl Miliańczuk, Marian Stanisław Puchalik, Antoni Wincenty Raabe, Stanisław Saks, Hugo Steinhaus, Zygmunt Zachorski, Miron Zarycki i Eustachy Żyliński. Do tej pory myśleliśmy, że zaginęły prace, ale na szczęście w archiwum znaleziono siedem rękopisów. Prezentujemy tytuły znalezionych artykułów z informacją, co będzie dalej z rękopisami.

Uwaga: W artykule na stronie 74 po [Z5] powinno być:[Z6] E. Żyliński, O gremowskiej transformacji macierzy prostokątnych, 30-62,  natomiast numery [Z6] - [Z17]^* powinny być numerowane jako [Z7] - [Z18]^*.

Abstract [en]

Contents of the Lvovian journal Scientific Notes of the Faculty of Mathematics and Physics from 1940 and 1941, which was found in archive is presented. Among authors were: Stefan Banach, Leon Chwistek, Meier Eidelheit, Gertwagen, Jan Hercberg, Marian Mojżesz Jacob, Salomon Lubelski, Jan Mergentaler, Wasyl Miliańczuk, Marian Stanisław Puchalik, Antoni Wincenty Raabe, Stanisław Saks, Hugo Steinhaus, Zygmunt Zachorski, Miron Zarycki and Eustachy Żyliński. Until now we thought that papers are lost but fortunately seven manuscripts were found in archive. We present the titles of found papers with the information what will happened next with the manuscripts.

 Note: In the article on page 74 after [Z5] should be:[Z6] E. Żyliński, O gremowskiej transformacji macierzy prostokątnych, 30-62,  while the numbers [Z6] - [Z17]^* should be numbered as [Z7] - [Z18]^*.

Place, publisher, year, edition, pages
Warszawa: , 2018
Keywords
Lvov University, unpublished papers, Uniwersytet we Lwowie, nieopublikowane prace
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-73516 (URN)
Available from: 2019-04-08 Created: 2019-04-08 Last updated: 2019-08-20Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9584-4083

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