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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Unicity of a holomorphic functional calculus in infinite dimensions


Author: José E. Galé
Journal: Trans. Amer. Math. Soc. 295 (1986), 501-508
MSC: Primary 46H30; Secondary 32A10, 46G20
MathSciNet review: 833694
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0833694-4
PII: S 0002-9947(1986)0833694-4
Keywords: Holomorphic functional calculus, infinite-dimensional holomorphy, weakly uniformly continuous functions, bounded approximation property
Article copyright: © Copyright 1986 American Mathematical Society