Operators on the L∞-spaces of Bourgain and Delbaen

Authors

Kevin Beanland
Lon Mitchell, University of South Florida St. PetersburgFollow

SelectedWorks Author Profiles:

Lon Mitchell

Document Type

Article

Publication Date

2010

ISSN

1607-3606 (Print) 1727-933X (Online)

Abstract

In 1980, J. Bourgain and F. Delbaen constructed two classes and of ∞-spaces each exhibiting many surprising properties. In particular, the members of each possess the Schur property and the members of are somewhat reflexive. In this paper, for a Banach space in either of these classes we define a bounded shift-type operator which is an isometry when restricted to a certain hyperplane.

Publisher

Taylor & Francis

Recommended Citation

Beanland, K. & Mitchell, L. (2010). Operators on the L ∞- spaces of Bourgain and Delbaen. Quaestiones Mathematicae, 33(4), 443-448. https://doi.org/10.2989/16073606.2010.541614.