Abstract
The algebras of continuous functions on a compact set which are called uniform, were introduced in connection with applications of methods of functional analysis in the classical theory of functions. Nowadays, the theory of uniform algebras is an independent branch of analysis which has its own objects and methods of investigation. Beginning from 70’s some interest on noncommutative analogues of uniform algebras arose and a few generalizing results were obtained, [13], [14], [12]. These algebras are some closed subalgebras of a C*-algebra of operator fields, introduced by Fell [7]. It seems natural to expect that the theory of noncommutative uniform algebras must include such standard notions as the maximal ideal space, Choquet boundary, maximality etc. It is not clear how legitimate are such formulations of questions for algebras with varying fibres. Our paper is an attempt to fulfil this program for a special case of uniform algebras of continuous C*-valued functions on a compact set. A series of papers is devoted to these subjects, [2], [3], [4], [5].
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© 1990 Birkhäuser Verlag Basel
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Arzumanian, V., Grigorian, S. (1990). Noncommutative Uniform Algebras. In: Helson, H., Sz.-Nagy, B., Vasilescu, FH., Arsene, G. (eds) Linear Operators in Function Spaces. Operator Theory: Advances and Applications, vol 43. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7250-8_5
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DOI: https://doi.org/10.1007/978-3-0348-7250-8_5
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