Some properties of space of compact operators

Narcisse Randrianantoanina

Some properties of space of compact operators

Functional Analysis 2016-09-06 v1

Authors: Narcisse Randrianantoanina

Abstract

Let $X$ be a separable Banach space, $Y$ be a Banach space and $\Lambda$ be a subset of the dual group of a given compact metrizable abelian group. We prove that if $X^*$ and $Y$ have the type I- $\Lambda$ -RNP (resp. type II- $\Lambda$ -RNP) then $K(X,Y)$ has the type I- $\Lambda$ -RNP (resp. type II- $\Lambda$ -RNP) provided $L(X,Y)=K(X,Y)$ . Some corollaries are then presented as well as results conserning the separability assumption on $X$ . Similar results for the NearRNP and the WeakRNP are also presented.

Keywords

compact operators Banach spaces type I-Λ-RNP type II-Λ-RNP NearRNP WeakRNP

Cite

@article{arxiv.math/9405211,
  title  = {Some properties of space of compact operators},
  author = {Narcisse Randrianantoanina},
  journal= {arXiv preprint arXiv:math/9405211},
  year   = {2016}
}

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