Local uniform convexity and Kadec-Klee type properties inK-interpolation spaces I: General Theory
نویسندگان
چکیده
منابع مشابه
On Semi-Uniform Kadec-Klee Banach Spaces
and Applied Analysis 3 We now introduce a property lying between U-space and semi-KK. Definition 1.8. We say that a Banach space X is semi-uniform Kadec-Klee if for every ε > 0 there exists a δ > 0 such that semi-UKK : {xn} ⊂ SX xn ⇀ x 〈 xn − x, fn 〉 ≥ ε, for some {fn } ⊂ SX∗ satisfying fn ∈ ∇xn ∀n ⎫ ⎪ ⎪⎬ ⎪ ⎪⎭ ⇒ ‖x‖ ≤ 1 − δ. 1.10 In this paper, we prove that semi-UKK property is a nice generali...
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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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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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We consider the notion of a uniformly concave function, using it to characterize those Lorentz spaces Lw,1 that have the weak-star uniform Kadec-Klee property as precisely those for which the antiderivative φ of w is uniformly concave; building on recent work of Dilworth and Hsu. We also derive a quite general sufficient condition for a twice-differentiable φ to be uniformly concave; and explor...
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ژورنال
عنوان ژورنال: Journal of Function Spaces and Applications
سال: 2004
ISSN: 0972-6802
DOI: 10.1155/2004/678358