Abstract
In this paper, we determine the character spaces and the Silov boundaries of A-valued Lipschitz algebras Lipα(X, A) and lipα(X, A) when X is a compact metric space, α ∈ (0, 1] and A is a commutative Banach algebta. We then consider the closed subalgebra LipP(K, A, α) of Lipα(K, A) which is generated by A-valued polynomials on a compact plane set K, and investigate the character space and the Silov boundary of this subalgebra.
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