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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Block diagonalization in Banach algebras


Author: Robin Harte
Journal: Proc. Amer. Math. Soc. 129 (2001), 181-190
MSC (1991): Primary 47A13; Secondary 15A21, 15A18
Published electronically: August 17, 2000
MathSciNet review: 1784022
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Abstract:

``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: http://dx.doi.org/10.1090/S0002-9939-00-05884-6
PII: S 0002-9939(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