Journal article
Analytic functions which operate on homogeneous algebras
Journal of the Australian Mathematical Society, Vol.45(01), pp.1-10
1988
Abstract
It is well known that a complex-valued function ø, analytic on some open set Ω, extends to any commutative Banach algebra B so that the action of ø on B commutes with the action of the Gelfand transformation. In this paper, it is shown that if B is a homogeneous convolution Banach algebra over any compact group and if 0 ϵ Ω is a fixed point of ø, then a similar result holds, with the Gelfand transformation replaced by the Fourier-Stieltjes transformation. Care is required, in that discussion of this relation usually requires simultaneous consideration of the extension of ø to B and to certain operator algebras.
Details
- Title
- Analytic functions which operate on homogeneous algebras
- Authors/Creators
- J.A. Ward (Author/Creator) - Murdoch University
- Publication Details
- Journal of the Australian Mathematical Society, Vol.45(01), pp.1-10
- Publisher
- Cambridge University Press
- Identifiers
- 991005545086407891
- Copyright
- © 1988, Australian Mathematical Society
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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- Citation topics
- 9 Mathematics
- 9.28 Pure Maths
- 9.28.886 Operator Algebras
- Web Of Science research areas
- Mathematics
- Statistics & Probability
- ESI research areas
- Mathematics