Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615368 | Journal of Mathematical Analysis and Applications | 2015 | 6 Pages |
Abstract
Let K be a simplex and let A0(K)A0(K) denote the space of continuous affine functions on K vanishing at a fixed extreme point, denoted by 0. We prove that if any extreme operator T from a Banach space X to A0(K)A0(K) is a nice operator (that is, T⁎T⁎, the adjoint of T , preserves extreme points), then the facial topology of the set of extreme points different from 0 is discrete, and so A0(K)A0(K) is isometrically isomorphic to c0(I)c0(I) for some set I . From here we derive the corresponding result for A(K)A(K), namely, if K is a simplex such that each extreme operator from any Banach space to A(K)A(K) is a nice operator, then the set of extreme points of K is finite.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Ana M. Cabrera-Serrano, Juan F. Mena-Jurado,