Algebras of free holomorphic functions and localizations
Copyright policy )Algebras of free holomorphic functions and localizations
Abstract We consider the algebras of holomorphic functions on a free polydisc , and the algebra of holomorphic functions on a free ball . We show that the algebra is a localization of a free algebra and, moreover, is a free analytic algebra with generators (in the sense of J. Taylor), while the algebra is not a localization of a free algebra. In addition we prove that the class of localizations of free algebras and the class of free analytic algebras are closed under the operation of the Arens-Michael free product. Bibliography: 21 titles.
Functional calculus for linear operators, Several-variable operator theory (spectral, Fredholm, etc.), Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), Arens-Michael free product, General theory of topological algebras, algebra of holomorphic functions on free ball, localization, free analytic algebra, algebra of holomorphic functions on free polydisc
Functional calculus for linear operators, Several-variable operator theory (spectral, Fredholm, etc.), Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), Arens-Michael free product, General theory of topological algebras, algebra of holomorphic functions on free ball, localization, free analytic algebra, algebra of holomorphic functions on free polydisc
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