# AN ALTERNATIVE DUNFORD-PETTIS PROPERTY FOR JB*-TRIPLES

@article{Acosta2001ANAD, title={AN ALTERNATIVE DUNFORD-PETTIS PROPERTY FOR JB*-TRIPLES}, author={Mar'ia D. Acosta and Antonio M. Peralta}, journal={Quarterly Journal of Mathematics}, year={2001}, volume={52}, pages={391-401} }

We study a property weaker than the Dunford–Pettis property, introduced by Freedman, in the case of a JB*-triple. It is shown that a JBW*-triple W has this property if, and only if, W is a Hilbert space (regarded as a type 1 or 4 Cartan factor) or W has the Dunford–Pettis property. As a consequence, we get that the JBW ∗ -triples satisfying the Kadec–Klee property are finitedimensional or Hilbert spaces (regarded as Cartan factor 1 or 4).

## 11 Citations

### The alternative Dunford-Pettis Property in the predual of a von Neumann algebra

- Mathematics
- 2001

Let A be a be a type II von Neumann algebra with predual A . We prove that A does not satisfy the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (’n)…

### The Dunford-Pettis and the Kadec-Klee properties on tensor products of JB*-triples

- Mathematics
- 2005

We recall that a Banach spaceX satisfies the Dunford-Pettis property (DPP) if every weakly compact operator T from X to another Banach space is completely continuous, i.e. T maps weakly Cauchy…

### The Alternative Dunford–Pettis Property, Conjugations and Real Forms of C*‐Algebras

- Mathematics
- 2002

Let τ be a conjugation, alias a conjugate linear isometry of order 2, on a complex Banach space X and let Xτ be the real form of X of τ‐fixed points. In contrast to the Dunford–Pettis property, the…

### On weak sequential convergence in JB -triple duals

- Mathematics
- 2004

We study various Banach space properties of the dual spaceE of a homo- geneous Banach space (alias, a JB -triple) E. For example, if all primitive M-ideals of E are maximal, we show that E has the…

### The Alternative Dunford–Pettis Property for Subspaces of the Compact Operators

- Mathematics
- 2006

A Banach space X has the alternative Dunford–Pettis property if for every weakly convergent sequences (xn) → x in X and (xn*) → 0 in X* with ||xn|| = ||x||= 1 we have (xn*(xn)) → 0. We get a…

### The alternative Dunford-Pettis property on projective tensor products

- Mathematics
- 2006

A Banach space X has the Dunford–Pettis property (DPP) if and only if whenever (xn) and (pn) are weakly null sequences in X and X*, respectively, we have pn(xn)→ 0. Freedman introduced a stricly…

### Unique Extension of Atomic Functionals of JB*-Triples

- Mathematics
- 2006

This thesis initiates and proceeds to develop a theory of unique norm preserving extensions of extreme dual ball functionals and their σ-convex sums, in the category of JB*-triples. All such…

### Geometric implications of the M(r,s)-properties and the uniform Kadec-Klee property in JB*-triples

- Mathematics
- 2016

We explore new implications of the $M(r,s)$ and $M^*(r,s)$ properties for Banach spaces. We show that a Banach space $X$ satisfying property $M(1,s)$ for some $0<s\leq 1$, admitting a point $x_{0}$…

### Some remarks on weak compactness in the dual space of a JB*-triple

- Mathematics
- 2006

We obtain several characterizations of the relatively weakly compact subsets of the predual of a JBW*-triple. As a consequence we describe the relatively weakly compact subsets of the predual of a…

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