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Diagonals of the Powers of an Operator on a Banach Lattice

Luxemburg, W. A. J. and de Pagter, B. and Schep, A. R. (1995) Diagonals of the Powers of an Operator on a Banach Lattice. In: Operator Theory in Function Spaces and Banach Lattices. Operator Theory Advances and Applications. No.75. Birkhäuser Basel , Basel, pp. 223-273. ISBN 9783034898966.

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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.

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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.
Series Name:Operator Theory Advances and Applications
Issue or Number:75
Record Number:CaltechAUTHORS:20181003-155855535
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90124
Deposited By: George Porter
Deposited On:08 Oct 2018 23:21
Last Modified:16 Nov 2021 00:41

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