On weak sequential convergence in JB*-triple duals

Leslie J. Bunce, and Antonio M. Peralta. "On weak sequential convergence in JB*-triple duals." Studia Mathematica 160.2 (2004): 117-127. <http://eudml.org/doc/285109>.

@article{LeslieJ2004,
abstract = {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.},
author = {Leslie J. Bunce, Antonio M. Peralta},
journal = {Studia Mathematica},
keywords = {alternative Dunford-Pettis property; Kadec-Klee property; dual space of homogeneous Banach space; JB-triple},
language = {eng},
number = {2},
pages = {117-127},
title = {On weak sequential convergence in JB*-triple duals},
url = {http://eudml.org/doc/285109},
volume = {160},
year = {2004},
}

TY - JOUR
AU - Leslie J. Bunce
AU - Antonio M. Peralta
TI - On weak sequential convergence in JB*-triple duals
JO - Studia Mathematica
PY - 2004
VL - 160
IS - 2
SP - 117
EP - 127
AB - 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.
LA - eng
KW - alternative Dunford-Pettis property; Kadec-Klee property; dual space of homogeneous Banach space; JB-triple
UR - http://eudml.org/doc/285109
ER -