A Dauns-Hofmann theorem for TAF-algebras

Author:
D. W. B. Somerset

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1379-1385

MSC (1991):
Primary 46K50, 47D25

DOI:
https://doi.org/10.1090/S0002-9939-99-04606-7

Published electronically:
January 28, 1999

MathSciNet review:
1616597

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Abstract: Let be a TAF-algebra, the centre of the ideal lattice of , and the space of meet-irreducible elements of , equipped with the hull-kernel 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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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:
https://doi.org/10.1090/S0002-9939-99-04606-7

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