Published 1995
| public
Book Section - Chapter
Diagonals of the Powers of an Operator on a Banach Lattice
Chicago
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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
- Eprint ID
- 90124
- Resolver ID
- CaltechAUTHORS:20181003-155855535
- Created
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2018-10-08Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field
- Series Name
- Operator Theory Advances and Applications
- Series Volume or Issue Number
- 75