The Pełczyński property for some uniform algebras
F. Delbaen (1979)
Studia Mathematica
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F. Delbaen (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.
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.
Grzesiak, Maciej (1992)
Mathematica Pannonica
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P. Wojtaszczyk (1979)
Studia Mathematica
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José Aguayo-Garrido (1998)
Annales mathématiques Blaise Pascal
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J. Bourgain (1984)
Studia Mathematica
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Wilkins, Dave (1995)
International Journal of Mathematics and Mathematical Sciences
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F. Delbaen (1977-1978)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Diómedes Bárcenas (1991)
Extracta Mathematicae
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Walden Freedman (1997)
Studia Mathematica
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An alternative to the Dunford-Pettis Property, called the DP1-property, is introduced. Its relationship to the Dunford-Pettis Property and other related properties is examined. It is shown that -direct sums of spaces with DP1 have DP1 if 1 ≤ p < ∞. It is also shown that for preduals of von Neumann algebras, DP1 is strictly weaker than the Dunford-Pettis Property, while for von Neumann algebras, the two properties are equivalent.