Uniformly factoring weakly compact operators

Let X and Y be separable Banach spaces. Suppose Y either has a shrinking basis or Y is isomorphic to C(2N) and A 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∈A factors...

Full description

Saved in:
Bibliographic Details
Published in:Journal of functional analysis 2014-03, Vol.266 (5), p.2921-2943
Main Authors: Beanland, Kevin, Freeman, Daniel
Format: Article
Language:English
Subjects:
Asplund operators
Factorization
Polish spaces
Weakly compact operators
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let X and Y be separable Banach spaces. Suppose Y either has a shrinking basis or Y is isomorphic to C(2N) and A 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∈A factors through Z. Likewise, we prove that if A⊂L(X,C(2N)) 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∈A factors through Z. Finally we prove a uniform version of this result in which we allow the domain and range spaces to vary.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2013.12.015