k-Uniform Rotundity of Lorentz–Orlicz Spaces

On the Weak Uniform Rotundity of Banach Spaces

1. Definitions and preliminaries. In this note, X and Y denote Banach spaces and X∗ and Y∗ denote the conjugate spaces of X and Y , respectively. Let A⊂X be a closed subset and X/A denote the quotient space. We use S(X) for the unit sphere in X and Plp (Xi) for the lp product space. We refer to [1, 3] for the following definitions and notations. For more recent treatment, one may see, for examp...

On 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...

Extreme Points and Rotundity of Orlicz-sobolev Spaces

Testing Non-uniform k-Wise Independent Distributions over Product Spaces

A discrete distribution D overΣ1 × · · · × Σn is called (non-uniform) k-wise independent if for anyset of k indexes{i1, . . . ,ik} and for any z1 ∈ Σi1 , . . . , zk ∈ Σik ,PrX∼D[Xi1 · · ·Xik = z1 · · · zk] =PrX∼D[Xi1 = z1] · · ·PrX∼D[Xik = zk]. We study the problem of testing (non-uniform) k-wiseindependent distributions over product spaces. For the uniform case ...

Strongly k-spaces

‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.