## Banach Journal of Mathematical Analysis

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

#### 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

https://projecteuclid.org/euclid.bjma/1381782096

Digital Object Identifier
doi:10.15352/bjma/1381782096

Mathematical Reviews number (MathSciNet)
MR3161691

Zentralblatt MATH identifier
1277.47028

#### 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