Spectral synthesis in the multiplier algebra of a C₀(X)-algebra

2012/10/11 by Archbold, R. J., Somerset, D. W. B.
#46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1210.3251

Abstract

Let A be a C₀(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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