Abstract view
Holomorphic Generation of Continuous Inverse Algebras


Published:20070201
Printed: Feb 2007
Abstract
We study complex commutative Banach algebras
(and, more generally, continuous
inverse algebras) in which the holomorphic functions of a fixed $n$tuple
of elements are dense. In particular, we characterize the compact subsets
of~$\C^n$ which appear as joint spectra of such $n$tuples. The
characterization is compared with several established notions of holomorphic
convexity by means of approximation
conditions.
Keywords: 
holomorphic functional calculus, commutative continuous inverse algebra, holomorphic convexity, Stein compacta, meromorphic convexity, holomorphic approximation
holomorphic functional calculus, commutative continuous inverse algebra, holomorphic convexity, Stein compacta, meromorphic convexity, holomorphic approximation

MSC Classifications: 
46H30, 32A38, 32E30, 41A20, 46J15 show english descriptions
Functional calculus in topological algebras [See also 47A60] Algebras of holomorphic functions [See also 30H05, 46J10, 46J15] Holomorphic and polynomial approximation, Runge pairs, interpolation Approximation by rational functions Banach algebras of differentiable or analytic functions, $H^p$spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]
46H30  Functional calculus in topological algebras [See also 47A60] 32A38  Algebras of holomorphic functions [See also 30H05, 46J10, 46J15] 32E30  Holomorphic and polynomial approximation, Runge pairs, interpolation 41A20  Approximation by rational functions 46J15  Banach algebras of differentiable or analytic functions, $H^p$spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]
