Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495547 | Journal of Functional Analysis | 2005 | 28 Pages |
Abstract
We study the semi-simplicity of the second dual of the Banach algebra of operators on a Banach space, B(E)â³, endowed with either Arens product. It was previously shown that if E is a Hilbert space, then B(E) is Arens regular and B(E)â³ is semi-simple. We show that for a large class of Banach spaces E, including subspaces of Lp spaces not isomorphic to a Hilbert space, B(E)â³ is not semi-simple. This is achieved by deriving a new representation of B(lp)â², and then constructing a member of the radical of B(lp)â³, for pâ 2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Matthew Daws, Charles Read,