Publication Date:
2016-12-01
Description:
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≤1 , admitting a point x 0 in its unit sphere at which the relative weak and norm topologies agree, satisfies the generalized Gossez–Lami Dozo property. We establish sufficient conditions, in terms of the (r,s) -Lipschitz weak * Kadec-Klee property on a Banach space X , to guarantee that its dual space satisfies the uniform Kadec-Klee property in the weak * topology. We determine appropriate conditions to assure that a Banach space X satisfies the (r,s) -Lipschitz weak * KKP. These results are applied to prove that every spin factor satisfies the UKK property, and consequently, the KKP and the UKK property are equivalent for real and complex JB * -triples.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
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