Geometric implications of the M (r, s)-properties and the uniform Kadec-Klee property in JB*-triples
نویسندگان
چکیده
منابع مشابه
Uniform Kadec-Klee Property in Banach Lattices
We prove that a Banach lattice X which does not contain the ln ∞uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology τ on X. In case the Banach lattice is purely atomic, the topology τ is the coordinatewise convergence topology. 1980 Mathematics Subject Classification: Primary 46B03, 46B42.
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In this paper we show that the Lorentz space Lw,1(0,∞) has the weak-star uniform Kadec-Klee property if and only if inf t>0 w(αt) w(t) > 1 and sup t>0 φ(αt) φ(t) < 1 for all α ∈ (0, 1),
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It is proved that L(`p, `q) has the KK property if and only if it has the UKK property if and only if 1 < q < 2 < p < ∞. It is also proved that L(c0, `1) has the UKK property and that L(c0, `q) can be renormed to have the weak-star UKK property if (and only if) 1 ≤ q < 2. In all other cases L(`p, `q) has no equivalent UKK norm. Finally, it is proved that none of these spaces is either strictly ...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2016
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/haw036