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TOTALLY NULL SETS FOR A(X)

Part of: Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  07 June 2012

LYNETTE J. BOOS
LYNETTE J. BOOS*
Affiliation:
Department of Mathematics and Computer Science, Providence College, Providence, RI 02918, USA (email: lboos@providence.edu)
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Abstract

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For a compact subset K of the boundary of a compact Hausdorff space X, six properties that K may have in relation to the algebra A(X) are considered. It is shown that in relation to the algebra A(Dn), where Dn denotes the n-dimensional polydisc, the property of being totally null is weaker than the other five properties. A general condition is given on the algebra A(X) which implies the existence of a totally null set that is not null, and several conditions are stated for A(X) , each of which is sufficient for a totally null set to be a null set.

Keywords

polydiscBanach algebratotally null setnull setGleason part

MSC classification

Secondary: 46J10: Banach algebras of continuous functions, function algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 108 - 114
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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