Unicity of a holomorphic functional calculus in infinite dimensions

Galé, José E.

doi:10.1090/S0002-9947-1986-0833694-4

Unicity of a holomorphic functional calculus in infinite dimensions
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by José E. Galé PDF

Trans. Amer. Math. Soc. 295 (1986), 501-508 Request permission

Abstract:

L. Waelbroeck gives a holomorphic functional calculus for Banach algebras and analytic functions on Banach spaces. The properties of this calculus extend the well-known properties for the case of several complex variables. In this last situation, W. Zame has obtained a theorem of unicity where the famous condition of compatibility is dropped. We obtain a theorem analogous to Zame’s for Waelbroeck’s calculus restricted to a certain algebra of germs of functions. We consider Banach spaces whose topological duals have the bounded approximation property. Also, results of the same kind as above are given for bornological algebras.

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Unas aplicaciones de un cálculo funcional holomorfo en dimensión infinita

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