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Isomorphism of uniform algebras on the 2-torus

Published online by Cambridge University Press:  16 May 2018

JUSTIN R. PETERS  and
PREECHAYA SANYATIT
JUSTIN R. PETERS
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa, IA 50011U.S.A. e-mail: peters@iastate.edu
PREECHAYA SANYATIT
Affiliation:
Department of Mathematics, Silpakorn University, Nakhon Pathom, 73000Thailand e-mail: sanyatit_p@silpakorn.edu
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Abstract

For α a positive irrational, let 𝛢α be the subalgebra of continuous functions on the two-torus whose Fourier transform vanishes at (m, n) if m+αn < 0. These algebras were studied by Wermer and others, who proved properties such as maximality and characterised the Gelfand space. One of the major themes of current work in operator algebras is classification, but none of the properties which were investigated earlier distinguished between 𝛢α and αβ, if β is another positive irrational. We address this question. We also determine the automorphism group of 𝛢α.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 1 , July 2019 , pp. 89 - 106
Copyright
Copyright © Cambridge Philosophical Society 2018 

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