Banach Journal of Mathematical Analysis

Absolutely summing operators on separable Lindenstrauss spaces as tree spaces and the bounded approximation property

Asvald Lima, Vegard Lima, and Eve Oja

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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.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 1 (2014), 190-210.

Dates
First available in Project Euclid: 14 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1381782096

Digital Object Identifier
doi:10.15352/bjma/1381782096

Mathematical Reviews number (MathSciNet)
MR3161691

Zentralblatt MATH identifier
1277.47028

Subjects
Primary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
Secondary: 46B20: Geometry and structure of normed linear spaces 46B25: Classical Banach spaces in the general theory 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47L05: Linear spaces of operators [See also 46A32 and 46B28] 47L20: Operator ideals [See also 47B10]

Keywords
Banach spaces Banach operator ideals bounded approximation properties Lindenstrauss spaces

Citation

Lima, Asvald; Lima, Vegard; Oja, Eve. Absolutely summing operators on separable Lindenstrauss spaces as tree spaces and the bounded approximation property. Banach J. Math. Anal. 8 (2014), no. 1, 190--210. doi:10.15352/bjma/1381782096. https://projecteuclid.org/euclid.bjma/1381782096


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