Spectral synthesis in the multiplier algebra of a C_0(X)-algebra

R. J. Archbold; D. W. B. Somerset

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arXiv · 1210.3251

Spectral synthesis in the multiplier algebra of a C_0(X)-algebra

R. J. Archbold·D. W. B. Somerset

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Abstract

Let A be a C_0(X)-algebra. Then the multiplier algebra M(A) is a C(Y)-algebra in a natural way, where Y is the Stone-Cech compactification of X. Each x in X gives rise to an ideal J_x of A and an ideal H_x of M(A). The ideal J_x is contained in H_x, and H_x is contained in the strict closure of J_x in M(A). This paper studies the problem of determining when H_x is equal to the strict closure of J_x. THis can be interpreted as a problem of spectral synthesis type.

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BibTeX RIS

R. J. Archbold, D. W. B. Somerset. 2012-10-11. Spectral synthesis in the multiplier algebra of a C_0(X)-algebra. https://arxiv.org/abs/1210.3251

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