Hostname: page-component-cb9f654ff-hqlzj Total loading time: 0 Render date: 2025-08-23T06:16:03.560Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Information

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

References

[1]Browder, A., Introduction to Function Algebras (W.A. Benjamin, New York, NY, 1969).Google Scholar
[2]Cole, B. and Gamelin, T. W., ‘Tight uniform algebras and algebras of analytic functions’, J. Funct. Anal. 46 (1982), 158–220.CrossRefGoogle Scholar
[3]Cole, B. and Range, R. M., ‘A-measures on complex manifolds and some applications’, J. Funct. Anal. 11 (1972), 393–400.CrossRefGoogle Scholar
[4]Gamelin, T. W., Uniform Algebras, 2nd edn (Chelsea Publishing, New York, NY, 1984).Google Scholar
[5]Henkin, G. M., ‘Banach spaces of analytic functions on the ball and on the bicylinder are not isomorphic’, Funct. Anal. Appl. 2 (1968), 334–341.CrossRefGoogle Scholar
[6]Rudin, W., Function Theory in Polydiscs (W. A. Benjamin, New York, NY, 1974).Google Scholar
[7]Rudin, W., Function Theory in the Unit Ball of ℂn, Grundlehren der mathematischen Wissenschaften, 241 (Springer, New York, NY, 1980).CrossRefGoogle Scholar
[8]Saccone, S., A Study of Strongly Tight Uniform Algebras, PhD Thesis, Brown University, Providence, RI, 1995.CrossRefGoogle Scholar
[9]Stout, E. L., The Theory of Uniform Algebras (Bogden and Quigley, Tarrytown on Hudson, NY, 1971).Google Scholar