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Displaying similar documents to “Banach space properties of strongly tight uniform algebras”

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.

The Kadec-Pełczyński-Rosenthal subsequence splitting lemma for JBW*-triple preduals

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.

An alternative Dunford-Pettis Property

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 ℓ p -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.