On weakly compact operators from some uniform algebras
P. Wojtaszczyk (1979)
Studia Mathematica
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P. Wojtaszczyk (1979)
Studia Mathematica
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Richard Aron, Pablo Galindo, Mikael Lindström (1997)
Studia Mathematica
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We prove that every weakly compact multiplicative linear continuous map from into 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 , where is the open unit ball of an infinite-dimensional Banach space E.
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),...
F. Delbaen (1979)
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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 of the corresponding functions in . These results are achieved by studying the homomorphisms...
Z. Semadeni (1963)
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Fernando Bombal Gordon (1986)
Extracta Mathematicae
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Antonio M. Peralta, Hermann Pfitzner (2015)
Studia Mathematica
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Any bounded sequence in an L¹-space admits a subsequence which can be written as the sum of a sequence of pairwise disjoint elements and a sequence which forms a uniformly integrable or equiintegrable (equivalently, a relatively weakly compact) set. This is known as the Kadec-Pełczyński-Rosenthal subsequence splitting lemma and has been generalized to preduals of von Neuman algebras and of JBW*-algebras. In this note we generalize it to JBW*-triple preduals.
Manuel González, Joaquín M. Gutiérrez (1990)
Extracta Mathematicae
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Many authors have recently studied compact and weakly compact homomorphisms between function algebras. Among them, Lindström and Llavona [2] treat weakly compact continuous homomorphisms between algebras of type C(T) when T is a completely regular Hausdorff space. Llavona asked wether the results in [2] are valid in the case of algebras of differentiable functions on Banach spaces. The purpose of this note is to give an affirmative answer to this question, by proving that...
Jesús M. Fernández Castillo, Fernando Sánchez (1993)
Revista Matemática de la Universidad Complutense de Madrid
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Jesús M. Martínez Castillo (1995)
Extracta Mathematicae
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