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...
The group of invertible elements of a commutative Banach algebra
The inverse spectral radius formula and removability of spectrum
The kh-socle of a commutative semisimple Banach algebra
Let be a commutative complex semisimple Banach algebra. Denote by the kernel of the hull of the socle of . In this work we give some new characterizations of this ideal in terms of minimal idempotents in . This allows us to show that a “result” from Riesz theory in commutative Banach algebras is not true.
The Maximal Ideal Space of a Banach Algebra of Multipliers.
The metric space , 0
The non-archimedean Corona problem
The non-archimedean space
The norm of uniform convergence on the -algebraic maximal spectrum of an algebra over a non-archimedean valuation field
The norm spectrum in certain classes of commutative Banach algebras
Let A be a commutative Banach algebra and let be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by , where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.
The Pełczyński property for some uniform algebras
The projective limit of the spaces
The range of Toeplitz operators on the ball.