### The holomorphic functional calculus as an operational calculus

L. Waelbroeck (1982)

Banach Center Publications

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L. Waelbroeck (1982)

Banach Center Publications

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M. M. Talabani (1982)

Colloquium Mathematicae

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Jacob Burbea (1988)

Annales Polonici Mathematici

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Thiago R. Alves (2014)

Studia Mathematica

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We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.

Linus Carlsson, Urban Cegrell, Anders Fällström (2007)

Annales Polonici Mathematici

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We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.

L. Waelbroeck (1983)

Studia Mathematica

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S. Levi (1982)

Banach Center Publications

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Ivan Cnop (1972)

Annales de l'institut Fourier

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This paper studies properties of a large class of algebras of holomorphic functions with bounded growth in several complex variables. The main result is useful in the applications. Using the symbolic calculus of L. Waelbroeck, it gives for instance a theorem of the “Nullstellensatz” type and approximation theorems.

Graham R. Allan (2007)

Banach Center Publications

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This paper gives some very elementary proofs of results of Aupetit, Ransford and others on the variation of the spectral radius of a holomorphic family of elements in a Banach algebra. There is also some brief discussion of a notorious unsolved problem in automatic continuity theory.

Verónica Dimant, Pablo Galindo, Manuel Maestre, Ignacio Zalduendo (2004)

Studia Mathematica

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We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.

Christoph Schmoeger (1993)

Mathematica Scandinavica

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Angeles Prieto Yerro (1990)

Extracta Mathematicae

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Let H be the space of all bounded holomorphic functions on the unit ball of the Banach space E. In this note we study the algebra homomorphisms on H which are strict continuous.

Donald Z. Spicer (1973)

Colloquium Mathematicae

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