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Published 1995 | Version public
Book Section - Chapter Metadata-only

Diagonals of the Powers of an Operator on a Banach Lattice

Creators

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon Delft University of Technology
  • 3. ROR icon University of South Carolina

Contributors

Abstract

This paper is devoted to a detailed study of the properties of the band projection D of the complete lattice ordered algebra L_r(E) of the regular (or order bounded) operators of a Dedekind complete Banach lattice E onto the center Z(E) of E. We recall that the center Z(E) is the commutative subalgebra of L_r(E) of all T satisfying |T| ≤ λI where I is the identity operator. In the finite dimensional case, with respect to the standard numerical basis, Z(E) is the algebra of all diagonal matrices. For this reason the band projection D is called the diagonal map of E.

Additional Information

© Birkhäuser Verlag Basel/Switzerland 1995. Dedicated to Professor Dr. A. C. Zaanen on the occasion of his eightieth birthday. The authors would like to express their gratitude t.o Phillipe Clément, who brought Kingman's book ([13]) and the theory of renewal sequences to their attention.

Additional details

Identifiers

Eprint ID
90124
Resolver ID
CaltechAUTHORS:20181003-155855535

Dates

Created
2018-10-08
Created from EPrint's datestamp field
Updated
2021-11-16
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Caltech Custom Metadata

Series Name
Operator Theory Advances and Applications
Series Volume or Issue Number
75