On the Weak Uniform Rotundity of Banach Spaces
نویسندگان
چکیده
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 example, [2].
منابع مشابه
Uniform Boundedness Principle for operators on hypervector spaces
The aim of this paper is to prove the Uniform Boundedness Principle and Banach-Steinhaus Theorem for anti linear operators and hence strong linear operators on Banach hypervector spaces. Also we prove the continuity of the product operation in such spaces.
متن کاملWeak convergence theorems for symmetric generalized hybrid mappings in uniformly convex Banach spaces
In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover, we prove some weak convergence theorems for such mappings by using Ishikawa iteration method in a uniformly convex Banach space.
متن کاملThe James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces
Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...
متن کاملArens Regularity and Weak Amenability of Certain Matrix Algebras
Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...
متن کاملWeak Banach-Saks property in the space of compact operators
For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$, it is shown that the strong Banach-Saks-ness of all evaluation operators on ${mathcal M}$ is a sufficient condition for the weak Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in Y^*$, the evaluation op...
متن کامل