On certain homomorphisms of quotients of group algebras

Karel de Leeuw; Yitzhak Katznelson

doi:10.1007/BF02759951

On certain homomorphisms of quotients of group algebras

Karel de Leeuw^*, Yitzhak Katznelson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let A be the algebra of functions on the circle group T={z: |z|=1} having absolutely convergent Fourier series. For a subset E of A, the algebra of restrictions to E of functions in A is denoted by A(E). It is shown that for sets that are "thick" in one of several senses, algebra homomorphisms of the A(E) having norm 1 must arise from point mappings having a certain amount of rigidity.

Original language	English
Pages (from-to)	120-126
Number of pages	7
Journal	Israel Journal of Mathematics
Volume	2
Issue number	2
DOIs	https://doi.org/10.1007/BF02759951
State	Published - Jun 1964
Externally published	Yes

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title = "On certain homomorphisms of quotients of group algebras",

abstract = "Let A be the algebra of functions on the circle group T=\{z: |z|=1\} having absolutely convergent Fourier series. For a subset E of A, the algebra of restrictions to E of functions in A is denoted by A(E). It is shown that for sets that are {"}thick{"} in one of several senses, algebra homomorphisms of the A(E) having norm 1 must arise from point mappings having a certain amount of rigidity.",

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year = "1964",

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AB - Let A be the algebra of functions on the circle group T={z: |z|=1} having absolutely convergent Fourier series. For a subset E of A, the algebra of restrictions to E of functions in A is denoted by A(E). It is shown that for sets that are "thick" in one of several senses, algebra homomorphisms of the A(E) having norm 1 must arise from point mappings having a certain amount of rigidity.

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On certain homomorphisms of quotients of group algebras

Abstract

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