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

Antonio M. Peralta; Hermann Pfitzner

Displaying similar documents to “The Kadec-Pełczyński-Rosenthal subsequence splitting lemma for JBW*-triple preduals”

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),...

Norm attaining bilinear forms on C*-algebras

J. Alaminos, R. Payá, A. R. Villena (2003)

Studia Mathematica

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We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.

The Pełczyński property for some uniform algebras

F. Delbaen (1979)

Studia Mathematica

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Dual Banach algebras: representations and injectivity

Matthew Daws (2007)

Studia Mathematica

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We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of...

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 $H^{\infty} (D)$ into $H^{\infty} (D)$ 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 $H^{\infty} (B_{E})$ , where $B_{E}$ is the open unit ball of an infinite-dimensional Banach space E.

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

J. Bourgain (1984)

Studia Mathematica

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On some classes of BCH-algebras.

Chaudhry, Muhammad Anwar, Fakhar-Ud-Din, Hafiz (2001)

International Journal of Mathematics and Mathematical Sciences

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Operators from C*-algebras to Banach Spaces.

J.D. Maitland Wright (1980)

Mathematische Zeitschrift

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An approach to Schreier's space.

Jesús M. Fernández Castillo, Manuel González (1991)

Extracta Mathematicae

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In 1930, J. Schreier [10] introduced the notion of admissibility in order to show that the now called weak-Banach-Saks property does not hold in every Banach space. A variation of this idea produced the Schreier's space (see [1],[2]). This is the space obtained by completion of the space of finite sequences with respect to the following norm: ||x||_S = sup_{(A admissible)} ∑_{j ∈ A} |x_j|, ...

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.

On weak Agassiz systems of algebras

Ewa Graczyńska, Andrzej Wroński (1978)

Colloquium Mathematicum

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Derivations into iterated duals of Banach algebras

H. Dales, F. Ghahramani, N. Grønbæek (1998)

Studia Mathematica

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We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space $A^{(n)}$ is zero; i.e., $ℋ^{1} (A, A^{(n)}) = 0$ . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable;...

On the weak amenability of ℬ(X)

A. Blanco (2010)

Studia Mathematica

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We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.

Uniformly continuous functionals on Banach algebras

Anthony To-Ming Lau (1987)

Colloquium Mathematicae

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A commutativity theorem for Banach algebras

Donald Z. Spicer (1973)

Colloquium Mathematicae

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Approximate identities in Banach function algebras

H. G. Dales, A. Ülger (2015)

Studia Mathematica

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In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractive Banach function algebra which is not equivalent to...