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Spectral mapping theorem for representations of measure algebras

Published online by Cambridge University Press:  20 January 2009

H. Seferoǧlu
H. Seferoǧlu
Affiliation:
Ondokuz Mayis University, Faculty of Arts and Sciences, Department of Mathematics, 55139, Kurupelit, Samsun, Turkey
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Abstract

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Let G be a locally compact abelian group, M0(G) be a closed regular subalgebra of the convolution measure algebra M(G) which contains the group algebra L1(G) and ω: M0(G) → B be a continuous homomorphism of M0(G) into the unital Banach algebra B (possibly noncommutative) such that ω(L1(G)) is without order with respect to B in the sense that if for all b ∈ B, b.ω(L1(G)) = {0} implies b = 0. We prove that if sp(ω) is a synthesis set for L1(G) then the equality holds for each μ ∈ M0(G), where sp(ω) denotes the Arveson spectrum of ω, σB(.) the usual spectrum in B, the Fourier-Stieltjes transform of μ.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 2 , June 1997 , pp. 261 - 266
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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