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Block diagonalization in Banach algebras
Author(s):
Robin
Harte
Journal:
Proc. Amer. Math. Soc.
129
(2001),
181-190.
MSC (1991):
Primary 47A13;
Secondary 15A21, 15A18
Posted:
August 17, 2000
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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:
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
Posted:
August 17, 2000
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
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