On weak sequential convergence in JB*-triple duals

Leslie J. Bunce, Antonio M. Peralta
2004 Studia Mathematica  
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
more » ... 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.
doi:10.4064/sm160-2-2 fatcat:s226ehl5tje3ldqeslo6wfg3gi