Tensor product of URM algbras
Tensor products of commutative Banach algebras.
Tensor Products of Weighted Bergman Spaces and Invariant Ha-Plitz Operators.
The analytic -capacity and the Cauchy integral
The Banach algebra of continuous bounded functions with separable support
We prove a commutative Gelfand-Naimark type theorem, by showing that the set of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space X (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to C₀(Y) for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y, which we explicitly construct as a subspace of the Stone-Čech compactification of X, is countably compact, and if X is non-separable,...
The Banach space H...(X, d, ...).I.
The Banach space H...(X, d, ...).II.
The Bourgain algebra of the disk algebra A(𝔻) and the algebra QA
It is shown that the Bourgain algebra of the disk algebra A() with respect to is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is .
The characteristic algebra of a polynomial covering map.
The compactum of a semi-simple commutative Banach algebra.
The Complex Stone-Weierstrass Property
The compact Hausdorff space X has the CSWP iff every subalgebra of C(X,ℂ) which separates points and contains the constant functions is dense in C(X,ℂ). Results of W. Rudin (1956) and Hoffman and Singer (1960) show that all scattered X have the CSWP and many non-scattered X fail the CSWP, but it was left open whether having the CSWP is just equivalent to being scattered. Here, we prove some general facts about the CSWP; in particular we show that if X is a compact ordered space,...
The differential equation y' = fy in the algebras H(D).
The dual of the Bergman space defined on a hyperbolic plane domain.
The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces
The exceptional sets for functions of the Bergman space in the unit ball
Let be a domain in . Given , set . If is a holomorphic and square-integrable function in , then the set of all such that is not square-integrable in has measure zero. We call this set the exceptional set for . In this Note we prove that whenever there exists a holomorphic square-integrable function in the unit ball in such that is the circle .
The fixed point property of unital abelian Banach algebras.
The Fourier algebra of SL(2,...)......, n...2, has no multiplier bounded approximate unit.
The Fréchet envelopes of vector-valued Smirnov classes
The generalized corona theorem.
The Gleason-Kahane-Zelazko theorem and function algebras
A theorem due to A. Gleason, J.-P. Kahane and W. Zelazko characterizes continuous characters within the space of all continuous linear forms of a locally multiplicatively convex, sequentially complete algebra. The present paper applies these results to investigate linear isometries of Banach algebras (with particular attention to normal uniform algebras) and of some locally multiplicatively convex algebras. The locally multiplicatively convex algebra of all holomorphic functions on a domain, will...