Original Articles

Operators on the _∞-spaces of Bourgain and Delbaen

Published in: Quaestiones Mathematicae
Volume 33 , issue 4 , 2010 , pages: 443–448

DOI: 10.2989/16073606.2010.541614

Author(s): Kevin Beanland Department of Mathematics and Applied Mathematics, USA , Lon Mitchell Department of Mathematics and Applied Mathematics, USA

Keywords: Primary , 46B28 , Primary , 46B28

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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.

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