The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces
author
Abstract:
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 the recent literature.
similar resources
On the James Type Constant and Von Neumann–jordan Constant for a Class of Banaś–fra̧czieck Type Spaces
As a generalization of Banaś-Fra̧czieck space, the space Xλ ,p that denotes R 2 endowed with the norm ‖x‖λ ,p = max{λ |x1 |,‖x‖p} for λ > 1 , p 1 and x = (x1,x2) ∈ R2 is well defined. In this note, the exact value of the the James type constants JXλ ,p ,t(1) and von Neumann-Jordan constant CNJ (Xλ ,p) about this space for p 2 are investigated.
full textOn Estimates of the Generalized Jordan-von Neumann Constant of Banach Spaces
In this paper, we study the generalized Jordan-von Neumann constant and obtain its estimates for the normal structure coefficient N(X), improving the known results of S. Dhompongsa.
full textThe uniform structure of Banach spaces
We explore the existence of uniformly continuous sections for quotient maps. Using this approach we are able to give a number of new examples in the theory of the uniform structure of Banach spaces. We show for example that there are two non-isomorphic separable L1-subspaces of 1 which are uniformly homeomorphic. We also prove the existence of two coarsely homeomorphic Banach spaces (i.e. with ...
full textVarious topological forms of Von Neumann regularity in Banach algebras
We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...
full textAN INEQUALITY ON JORDAN–VON NEUMANN CONSTANT AND JAMES CONSTANT ON Zp,q SPACE
Let λ > 0 , Zp,q denote R2 endowed with the norm |x|p,q = (‖x‖p +λ‖x‖q) 1 2 . Recently, James constant J(Zp,q) and von Neumann-Jordan constant CNJ(Zp,q) have been investigated under the two cases of a space 2 p q ∞ and 1 p q 2 . In this note, we show an inequality on these two constants under the case of 1 p 2 q ∞ . As an application, we give a sufficient condition for the space Zp,q with unifo...
full textMy Resources
Journal title
volume 8 issue 1
pages 113- 122
publication date 2017-06-05
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023