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Existence and uniqueness of functional calculus homomorphisms

1976
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Bulletin of the American Mathematical Society
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The purpose of this note is to announce a uniqueness result for the holomorphic functional calculus in commutative Banach algebras which is much stronger than the usual uniqueness assertion. Let A be a commutative Banach algebra with unit and let a = (a 1 , . . . , a n ) be an «-tuple of elements of A. Denote by a(a) the joint spectrum of a and by ö(a(a)) the topological algebra of germs of functions holomorphic near a(a). The holomorphic functional calculus, developed by Shilov [6],

doi:10.1090/s0002-9904-1976-13987-0
fatcat:o72akwab4vdanowwejlpscse7y