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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-2-2,
author = {Leslie J. Bunce and Antonio M. Peralta},
title = {On weak sequential convergence in JB*-triple duals},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {117-127},
zbl = {1123.46054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-2-2}
}
Leslie J. Bunce; Antonio M. Peralta. On weak sequential convergence in JB*-triple duals. Studia Mathematica, Tome 162 (2004) pp. 117-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-2-2/