On the OrliczCesaro sequence spaces ( ces ) which are defined by using Orlicz function , we show that the space ces equipped with both Amemiya and Luxemburg norms possesses uniform Opial property and uniform Kadec-Klee property if satisfy the 52 -condition.

Abstract The necessary and sufficient conditions for both the Kadec–Klee property as well with respect to coordinatewise convergence in Orlicz–Lorentz sequence spaces equipped Orlicz norm generated by arbitrary functions any non-increasing weight sequences are given. Moreover, their subspaces of elements an order continuous full characterization is presented. Some tools useful proofs main resul...

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),

We define the concepts of stable sampling set, interpolation uniqueness set and complete for a quasinormed space functions apply these to Paley-Wiener spaces Bernstein spaces. obtain sufficient condition on uniformly discrete be an based lemma convergence series in also result transference, Kadec type, property being from with this other which we