Spectral synthesis in the multiplier algebra of a C0(X)-algebra
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 Jx of A and an ideal Hx of M(A). The ideal Jx is contained in Hx, and Hx is contained in the strict closure of Jx in M(A). This paper studies the problem of determining when Hx is equal to the strict closure of Jx. THis can be interpreted as a problem of spectral synthesis type.
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