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2014 Absolutely summing operators on separable Lindenstrauss spaces as tree spaces and the bounded approximation property
Asvald Lima, Vegard Lima, Eve Oja
Banach J. Math. Anal. 8(1): 190-210 (2014). DOI: 10.15352/bjma/1381782096

Abstract

Let $X$ be a Banach space and let $Y$ be a separable Lindenstrauss space. We describe the Banach space $\mathcal{P}(Y,X)$ of absolutely summing operators as a general $\ell_1$-tree space. We also characterize the bounded approximation property and its weak version for $X$ in terms of the space of integral operators $\mathcal{I}(X,Z^*)$ and the space of nuclear operators $\mathcal{N}(X,Z^*)$, respectively, where $Z$ is a Lindenstrauss space, whose dual $Z^*$ fails to have the Radon-Nikodým property.

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Asvald Lima. Vegard Lima. Eve Oja. "Absolutely summing operators on separable Lindenstrauss spaces as tree spaces and the bounded approximation property." Banach J. Math. Anal. 8 (1) 190 - 210, 2014. https://doi.org/10.15352/bjma/1381782096

Information

Published: 2014
First available in Project Euclid: 14 October 2013

zbMATH: 1277.47028
MathSciNet: MR3161691
Digital Object Identifier: 10.15352/bjma/1381782096

Subjects:
Primary: 47B10
Secondary: 46B20, 46B25, 46B28, 46E30, 47L05, 47L20

Rights: Copyright © 2014 Tusi Mathematical Research Group

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Vol.8 • No. 1 • 2014
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