Operators on the L∞-spaces of Bourgain and Delbaen
1607-3606 (Print) 1727-933X (Online)
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.
Taylor & Francis
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.