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.
Citation
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
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