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It is shown that the Bourgain algebra $A {()}_{b}$ of the disk algebra A() with respect to $H^{\infty} ()$ is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to $H^{\infty} ()$ , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is $A {()}_{b}$ .

The differential equation y' = fy in the algebras H(D).

Alain Escassut, Marie-Claude Sarmant (1988)

Collectanea Mathematica

The dual of the Bergman space defined on a hyperbolic plane domain.

Mateljević, Miodrag (1994)

Publications de l'Institut Mathématique. Nouvelle Série

The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces

J. Bourgain (1984)

Studia Mathematica

The exceptional sets for functions of the Bergman space in the unit ball

Piotr Jakóbczak (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $D$ be a domain in $C^{2}$ . Given $w \in C$ , set $D_{w} = \{z \in C ∣ (z, w) \in D\}$ . If $f$ is a holomorphic and square-integrable function in $D$ , then the set $E (D, f)$ of all $w$ such that $f (\cdot, w)$ is not square-integrable in $D_{w}$ has measure zero. We call this set the exceptional set for $f$ . In this Note we prove that whenever $0 < r < 1$ there exists a holomorphic square-integrable function $f$ in the unit ball $B$ in $C^{2}$ such that $E (B, f)$ is the circle $C (0, r) = \{z \in C ∣ |z| = r\}$ .

The Fréchet envelopes of vector-valued Smirnov classes

M. Nawrocki (1989)

Studia Mathematica

The generalized corona theorem.

P. Gorkin, R. Mortini, A. Nicolau (1995)

Mathematische Annalen

The Gleason-Kahane-Zelazko theorem and function algebras

Edoardo Vesentini (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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 metric space $H^{p} (A)$ , 0

David M. Boyd (1978)

Colloquium Mathematicae

The non-archimedean Corona problem

Marius van der Put (1974)

Mémoires de la Société Mathématique de France

The norm of uniform convergence on the $k$ -algebraic maximal spectrum of an algebra over a non-archimedean valuation field $k$

Ulrich Güntzer (1974)

Mémoires de la Société Mathématique de France

Currently displaying 1 – 20 of 31

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Displaying 1 – 20 of 31

Tensor Products of Weighted Bergman Spaces and Invariant Ha-Plitz Operators.

The analytic $α$ -capacity and the Cauchy integral

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

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

The Fréchet envelopes of vector-valued Smirnov classes

The generalized corona theorem.

The Gleason-Kahane-Zelazko theorem and function algebras

The metric space $H^{p} (A)$ , 0

The non-archimedean Corona problem

The norm of uniform convergence on the $k$ -algebraic maximal spectrum of an algebra over a non-archimedean valuation field $k$

The projective limit of the $H^{p}$ spaces

The range of Toeplitz operators on the ball.

The space of multipliers into $l_{1}$

The structure of homomorphisms from Banach algebras of differentiable functions into finite dimensional Banach algebras.

The structure of ideals in the Banach algebra of Lipschitz functions over valued fields

Currently displaying 1 – 20 of 31