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A new characterization of Bergman-Schatten spaces and a duality result
Technical University of Civil Engineering Bucharest.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Technical University of Civil Engineering Bucharest.
University of Bucharest and Institute of Mathematics of Romanian Academy.
2009 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 360, no 1, p. 67-80Article in journal (Refereed) Published
Abstract [en]

Let B0 (D, ℓ2) denote the space of all upper triangular matrices A such that limr → 1- (1 - r2) {norm of matrix} (A * C (r))′ {norm of matrix}B (ℓ2) = 0. We also denote by B0, c (D, ℓ2) the closed Banach subspace of B0 (D, ℓ2) consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between B0, c (D, ℓ2) and the Bergman-Schatten spaces La1 (D, ℓ2). We also give a characterization of the more general Bergman-Schatten spaces Lap (D, ℓ2), 1 ≤ p < ∞, in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, Lp-behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219-237] for classical Bergman spaces.

Place, publisher, year, edition, pages
2009. Vol. 360, no 1, p. 67-80
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-6808DOI: 10.1016/j.jmaa.2009.06.027ISI: 000269020900007Scopus ID: 2-s2.0-68249101588Local ID: 519d6150-5d7c-11de-9f57-000ea68e967bOAI: oai:DiVA.org:ltu-6808DiVA, id: diva2:979694
Note
Validerad; 2009; 20090620 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Persson, Lars-Erik

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