Kadec-Klee properties of Calderón-Lozanovskiĭ sequence spaces
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 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 کاملKADEC-KLEE PROPERTIES FOR L(`p, `q)
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 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...
متن کاملOn a Property of Kadec-klee Type for Quasi-normed Unitary Matrix Spaces
We say that the quasi-norm Φ of a symmetric sequence space E has property P if, for all x, y ∈ E with 0 ≤ xn ≤ yn for all n, and xN < yN for some N , we have Φ (xn) < Φ (yn) . Simon [6] proved that if the Banach norm Φ has property P , then whenever An → A in the weak operator topology on the unitary matrix space CE and Φ(An)→ Φ(A), then An → A in the strong operator topology on CE . In this no...
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ژورنال
عنوان ژورنال: Collectanea Mathematica
سال: 2010
ISSN: 0010-0757,2038-4815
DOI: 10.1007/s13348-010-0015-7