Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589948 | Journal of Functional Analysis | 2015 | 19 Pages |
Abstract
Let X be a Banach space and let Y be a closed subspace of a Banach space Z. Let α be a tensor norm. Our main result is as follows. Assume that X⁎X⁎ or Z⁎Z⁎ has the approximation property. If there is a bounded linear extension operator from Y⁎Y⁎ to Z⁎Z⁎, then any bounded linear operator T:X→YT:X→Y is α-nuclear whenever T is α-nuclear from X to Z . Using this result, we characterize the space Cp(Ω,X)Cp(Ω,X) (respectively, UCp(Ω,X)UCp(Ω,X)) of continuous functions from a compact Hausdorff space Ω into a Banach space X whose range is p-compact (respectively, unconditionally p-compact).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Fernando Muñoz, Eve Oja, Cándido Piñeiro,