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On weak sequential convergence in JB*-triple duals

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Bunce L., Peralta A.

Studia Mathematica

2004

tom 160

nr 2

117-127

We study various Banach space properties of the dual space E* of a homogeneous Banach space (alias, a JB*-triple) E. For example, if all primitive M-ideals of E are maximal, we show that E* has the Alternative Dunford-Pettis property (respectively, the Kadec-Klee property) if and only if all biholomorphic automorphisms of the open unit ball of E are sequentially weakly continuous (respectively, weakly continuous). Those E for which E* has the weak* Kadec-Klee property are characterised by a compactness condition on E. Whenever it exists, the predual of E is shown to have the Kadec-Klee property if and only if E is atomic with no infinite spin part.

Ograniczanie wyników

1 Studia Mathematica

1 Bunce L.

1 Peralta A.

1 2004

Wyniki wyszukiwania

On weak sequential convergence in JB*-triple duals