Displaying similar documents to “Holomorphic functional calculus and quotient Banach algebras”

Spectrum of certain Banach algebras and ∂̅-problems

Linus Carlsson, Urban Cegrell, Anders Fällström (2007)

Annales Polonici Mathematici


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.

Spectral study of holomorphic functions with bounded growth

Ivan Cnop (1972)

Annales de l'institut Fourier


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.

Some simple proofs in holomorphic spectral theory

Graham R. Allan (2007)

Banach Center Publications


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.

Integral holomorphic functions

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

Studia Mathematica


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.