This is an announcement for the paper "Uniformly factoring weakly compact operators" by Kevin Beanland and Daniel Freeman.

Abstract: Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either has a shrinking basis or $Y$ is isomorphic to $C(2^\nn)$ and $\aaa$ is a subset of weakly compact operators from $X$ to $Y$ which is analytic in the strong operator topology. We prove that there is a reflexive space with a basis $Z$ such that every $T \in \aaa$ factors through $Z$. Likewise, we prove that if $\aaa \subset \llll(X, C(2^\nn))$ is a set of operators whose adjoints have separable range and is analytic in the strong operator topology then there is a Banach space $Z$ with separable dual such that every $T \in \aaa$ factors through $Z$. Finally we prove a uniformly version of this result in which we allow the domain and range spaces to vary.

Archive classification: math.FA

Remarks: 19 pages, comments welcome

Submitted from: kbeanland@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1304.3471

or

http://arXiv.org/abs/1304.3471