Abstract

We consider vector-valued Banach function algebras on a compact Hausdorff space. Then, we define the subalgebras generated by vector-valued polynomials and rational functions, and determine their maximal ideal spaces and Silov boundaries. We finally make use the results for a certain category of these algebras such as vector-valued Lipschitz algebras, vector-valued Dales–Davie algebras (algebras of vector-valued differentiable functions) and the algebras of vector-valued differentiable Lipschitz functions.

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