Block diagonalization in Banach algebras

Author:
Robin Harte

Journal:
Proc. Amer. Math. Soc. **129** (2001), 181-190

MSC (1991):
Primary 47A13; Secondary 15A21, 15A18

DOI:
https://doi.org/10.1090/S0002-9939-00-05884-6

Published electronically:
August 17, 2000

MathSciNet review:
1784022

Full-text PDF

Abstract | References | Similar Articles | Additional Information

``Reduction" of linear operators is effected by commuting projections; the spectrum of the operator is then the union of the spectra of its range and null space restrictions. Disjointness of these partial spectra implies that the projection ``double commutes" with the operator, which in turn can be recognised as a curious kind of ``exactness". Variants of this exactness correspond to various kinds of disjointness between the partial spectra.

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Additional Information

**Robin Harte**

Affiliation:
School of Mathematics, Trinity College, Dublin 2, Ireland

Email:
rharte@maths.tcd.ie

DOI:
https://doi.org/10.1090/S0002-9939-00-05884-6

Keywords:
Commuting idempotent,
double commutant,
spectral disjointness,
exactness conditions

Received by editor(s):
December 15, 1997

Received by editor(s) in revised form:
March 10, 1998, October 6, 1998, and March 31, 1999

Published electronically:
August 17, 2000

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society