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Astashkin, Sergey
Alternative names
Publications (8 of 8) Show all publications
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
Astashkin, S. & Maligranda, L. (2010). Rademacher functions in Cesaro type spaces (ed.). Paper presented at . Studia Mathematica, 198(3), 235-247
Open this publication in new window or tab >>Rademacher functions in Cesaro type spaces
2010 (English)In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 198, no 3, p. 235-247Article in journal (Refereed) Published
Abstract [en]

The Rademacher sums are investigated in the Cesaro spaces Ces(p) (1 <= p <= infinity) and in the weighted Korenblyum-Krein-Levin spaces K-p,K-w on [0,1]. They span l(2) space in Ces(p) for any 1 <= p < infinity and in K-p,K-w if and only if the weight w is larger than t log(2)(p/2)(2/t) on (0,1). Moreover, the span of the Rademachers is not complemented in Ces(p) for any 1 <= p < infinity or in K-1,K-w for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l(2), this span is a complemented subspace in K-p,K-w.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-4680 (URN)10.4064/sm198-3-3 (DOI)000278741000003 ()2-s2.0-77954491031 (Scopus ID)2a935230-821b-11df-ab16-000ea68e967b (Local ID)2a935230-821b-11df-ab16-000ea68e967b (Archive number)2a935230-821b-11df-ab16-000ea68e967b (OAI)
Note
Validerad; 2010; 20100627 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Astashkin, S. & Maligranda, L. (2009). Structure of Cesaro function spaces (ed.). Paper presented at . Indagationes mathematicae, 20(3), 329-379
Open this publication in new window or tab >>Structure of Cesaro function spaces
2009 (English)In: Indagationes mathematicae, ISSN 0019-3577, E-ISSN 1872-6100, Vol. 20, no 3, p. 329-379Article in journal (Refereed) Published
Abstract [en]

The structure of the Cesàro function spaces Cesp on both [0,1] and [0, ∞) for 1 < p ≤ ∞ is investigated. We find their dual spaces, which equivalent norms have different description on [0, 1] and [0, ∞).The spaces Cesp for 1 < p < ∞ are not reflexive but strictly convex. They are not isomorphic to any Lq space with 1 ≤ q ≤ ∞. They have "near zero" complemented subspaces isomorphic to lp and "in the middle" contain an asymptotically isometric copy of l1 and also a copy of L1[0, 1]. They do not have Dunford-Pettis property but they do have the weak Banach-Saks property. Cesàro function spaces on [0, 1] and [0, ∞) are isomorphic for 1 < p ≤ ∞. Moreover, we give characterizations in terms of p and q when Cesp[0, 1] contains an isomorphic copy of lq.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-3377 (URN)10.1016/S0019-3577(10)00002-9 (DOI)000277755100001 ()2-s2.0-77952270739 (Scopus ID)132d5c00-5208-11df-a0f4-000ea68e967b (Local ID)132d5c00-5208-11df-a0f4-000ea68e967b (Archive number)132d5c00-5208-11df-a0f4-000ea68e967b (OAI)
Note
Validerad; 2010; 20100427 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Astashkin, S. & Maligranda, L. (2008). Cesaro function spaces fail the fixed point property (ed.). Paper presented at . Proceedings of the American Mathematical Society, 136(12), 4289-4294
Open this publication in new window or tab >>Cesaro function spaces fail the fixed point property
2008 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 12, p. 4289-4294Article in journal (Refereed) Published
Abstract [en]

The Cesaro sequence spaces ces(p), 1 < p < infinity, are reflexive but they have the fixed point property. In this paper we prove that in contrast to these sequence spaces the corresponding Cesaro function spaces Ces(p) on both [0, 1] and [0, infinity) for 1 < p < infinity are not reflexive and they fail to have the fixed point property.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-10410 (URN)93800e70-8658-11dd-8275-000ea68e967b (Local ID)93800e70-8658-11dd-8275-000ea68e967b (Archive number)93800e70-8658-11dd-8275-000ea68e967b (OAI)
Note
Validerad; 2008; 20080919 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
Astashkin, S. & Maligranda, L. (2008). Ultrasymmetric Orlicz spaces (ed.). Paper presented at . Journal of Mathematical Analysis and Applications, 347(1), 273-285
Open this publication in new window or tab >>Ultrasymmetric Orlicz spaces
2008 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 347, no 1, p. 273-285Article in journal (Refereed) Published
Abstract [en]

It is proved that ultrasymmetric reflexive Orlicz spaces can be described exactly as all those Orlicz spaces which can be written as some Lorentz spaces. This description is an answer to the problem posed by Pustylnik in [E. Pustylnik, Ultrasymmetric spaces, J. London Math. Soc. (2) 68 (1) (2003) 165-182]. On the other hand, the Lorentz-Orlicz spaces with non-trivial indices of their fundamental functions are ultrasymmetric.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-2747 (URN)10.1016/j.jmaa.2008.05.065 (DOI)000257914800025 ()2-s2.0-46449138269 (Scopus ID)06fb3970-7348-11dd-a60f-000ea68e967b (Local ID)06fb3970-7348-11dd-a60f-000ea68e967b (Archive number)06fb3970-7348-11dd-a60f-000ea68e967b (OAI)
Note
Validerad; 2008; 20080826 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Astashkin, S. & Maligranda, L. (2004). Interpolation between L1 and Lp, 1 (ed.). Paper presented at . Proceedings of the American Mathematical Society, 132(10), 2929-2938
Open this publication in new window or tab >>Interpolation between L1 and Lp, 1
2004 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 132, no 10, p. 2929-2938Article in journal (Refereed) Published
Abstract [en]

The main result of this paper is that if $X$ is an interpolation rearrangement invariant space on $[0,1]$ between $L_1$ and $L_\infty$, for which the Boyd index $\alpha(X)>1/p$, $1

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-15478 (URN)10.1090/S0002-9939-04-07425-8 (DOI)000222122800015 ()2-s2.0-5644237939 (Scopus ID)efead670-a7d1-11db-aeba-000ea68e967b (Local ID)efead670-a7d1-11db-aeba-000ea68e967b (Archive number)efead670-a7d1-11db-aeba-000ea68e967b (OAI)
Note
Validerad; 2004; 20070117 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Astashkin, S. V., Maligranda, L. & Semenov, E. M. (2003). Multiplicator space and complemented subspaces of rearrangement invariant space (ed.). Paper presented at . Journal of Functional Analysis, 202(1), 247-276
Open this publication in new window or tab >>Multiplicator space and complemented subspaces of rearrangement invariant space
2003 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 202, no 1, p. 247-276Article in journal (Refereed) Published
Abstract [en]

We show that the multiplicator space M(X) of an rearrangement invariant (r.i.) space X on [0, 1] and the nice part N0 (X) of X, that is, the set of all a ∈ X for which the subspaces generated by sequences of dilations and translations of a are uniformly complemented, coincide when the space X is separable. In the general case, the nice part is larger than the multiplicator space. Several examples of descriptions of M(X) and N0(X) for concrete X are presented

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-2745 (URN)10.1016/S0022-1236(02)00094-0 (DOI)000184296100011 ()2-s2.0-0043231680 (Scopus ID)06f58240-a9fb-11db-aeba-000ea68e967b (Local ID)06f58240-a9fb-11db-aeba-000ea68e967b (Archive number)06f58240-a9fb-11db-aeba-000ea68e967b (OAI)
Note
Validerad; 2003; 20070122 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Astashkin, S., Maligranda, L. & Semenov, E. (2002). On the complementness of subspaces generated by contractions and shifts of functions. (Russian) (ed.). Paper presented at . Doklady Akademii Nauk, 387(5), 583-585
Open this publication in new window or tab >>On the complementness of subspaces generated by contractions and shifts of functions. (Russian)
2002 (Russian)In: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 387, no 5, p. 583-585Article in journal (Refereed) Published
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-14372 (URN)db903760-aaf6-11db-aeba-000ea68e967b (Local ID)db903760-aaf6-11db-aeba-000ea68e967b (Archive number)db903760-aaf6-11db-aeba-000ea68e967b (OAI)
Note
Validerad; 2002; 20070123 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved
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