A DaunsHofmann theorem for TAFalgebras
Author:
D. W. B. Somerset
Journal:
Proc. Amer. Math. Soc. 127 (1999), 13791385
MSC (1991):
Primary 46K50, 47D25
Published electronically:
January 28, 1999
MathSciNet review:
1616597
Fulltext PDF Free Access
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Abstract: Let be a TAFalgebra, the centre of the ideal lattice of , and the space of meetirreducible elements of , equipped with the hullkernel topology. It is shown that is a compact, locally compact, second countable, space, that is an algebraic lattice isomorphic to the lattice of open subsets of , and that is isomorphic to the algebra of continuous, complex functions on . If is semisimple, then is isomorphic to the algebra of continuous, complex functions on , the primitive ideal space of . If is strongly maximal, then the sum of two closed ideals of is closed.
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 P. G. Dixon, Nonclosed sums of closed ideals in Banach algebras, preprint.
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 A. P. Donsig, T. D. Hudson, On the lattice of ideals of triangular AF algebras, J. Funct. Anal., 138 (1996), 139. MR 97e:47068
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 G. Gierz, K. H. Hofmann, K. Keimel, J. Lawson, M. Mislove, D. S. Scott, A Compendium of Continuous Lattices, SpringerVerlag, New York, 1980.MR 82h:06005
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 T. D. Hudson, Radicals and prime ideals in limit subalgebras of AF algebras, Quart. J. Math. Oxford (2) 48 (1997), 213233. MR 98i:46053
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 T. D. Hudson, E. G. Katsoulis, Primitive triangular UHF algebras, J. Funct. Anal., to appear.
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 M. P. Lamoureux, The topology of ideals in some triangular AF algebras, J. Operator Theory 37 (1997), 91109. CMP 97:04
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 , Ideal spaces of Banach algebras, Proc. London Math. Soc., to appear.
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 D. A. Stegenga, Ideals in the disk algebra, J. Funct. Anal. 25 (1977), 335337. MR 58:2307
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Additional Information
D. W. B. Somerset
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, AB24 UE United Kingdom
Email:
ds@maths.abdn.ac.uk
DOI:
http://dx.doi.org/10.1090/S0002993999046067
PII:
S 00029939(99)046067
Received by editor(s):
December 20, 1996
Received by editor(s) in revised form:
May 13, 1997, and August 7, 1997
Published electronically:
January 28, 1999
Communicated by:
Dale Alspach
Article copyright:
© Copyright 1999
American Mathematical Society
