Displaying similar documents to “On weakly compact operators from some uniform algebras”

Algebras of real analytic functions: Homomorphisms and bounding sets

Peter Biström, Jesús Jaramillo, Mikael Lindström (1995)

Studia Mathematica

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This article deals with bounding sets in real Banach spaces E with respect to the functions in A(E), the algebra of real analytic functions on E, as well as to various subalgebras of A(E). These bounding sets are shown to be relatively weakly compact and the question whether they are always relatively compact in the norm topology is reduced to the study of the action on the set of unit vectors in l ∞ of the corresponding functions in A ( l ∞ ) . These results are achieved by studying the homomorphisms...

Banach space properties of strongly tight uniform algebras

Scott Saccone (1995)

Studia Mathematica

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We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K),...

Compact homomorphisms between algebras of analytic functions

Richard Aron, Pablo Galindo, Mikael Lindström (1997)

Studia Mathematica

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We prove that every weakly compact multiplicative linear continuous map from H ∞ ( D ) into H ∞ ( D ) is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra H ∞ ( B E ) , where B E is the open unit ball of an infinite-dimensional Banach space E.