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...
متن کاملUniform 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.
متن کاملBanach Spaces Which Admit a Norm with the Uniform Kadec-klee Property
Several results are established about Banach spaces X which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from X to the Lebesgue-Bochner space L2(X) if and only if X is super-re exive. A basis characterization of the renorming property for dual Banach spaces is g...
متن کاملOn uniform Kadec-Klee properties and rotundity in generalized Cesàro sequence spaces
We consider the generalized Cesàro sequence spaces defined by Suantai (2003) and consider it equipped with the Amemiya norm. The main purpose of this paper is to show that ces (p) equipped with the Amemiya norm is rotund and has uniform Kadec-Klee property. 1. Introduction. In the whole paper, N and R stand for the sets of natural numbers and real numbers, respectively. Let (X, · ·) be a real n...
متن کاملA variational principle in reflexive spaces with Kadec-Klee norm
We prove a variational principle in reflexive Banach spaces X with KadecKlee norm, which asserts that any Lipschitz (or any proper lower semicontinuous bounded from below extended real-valued) function in X can be perturbed with a parabola in such a way that the perturbed function attains its infimum (even more can be said — the infimum is well-posed). In addition, we have genericity of the poi...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2010
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2010/652521