scholarly journals Order Uniform Convexity in Banach spaces with an application

2020 ◽  
pp. 1
Author(s):  
Monther R. Alfuraidan ◽  
Khamsi A. Mohamed
Keyword(s):  
Banach Spaces ◽  
Uniform Convexity

Complex convexity and the geometry of Banach spaces

1986 ◽  
Vol 99 (3) ◽  
pp. 495-506 ◽  
Author(s):  
S. J. Dilworth
Keyword(s):  
Banach Spaces ◽  
Present Article ◽  
Uniform Convexity ◽  
Unconditional Convergence

The notion of PL-convexity was introduced in [4]. In the present article several results are proved which related PL-convexity to various aspects of the geometry of Banach spaces. The first section introduces the moduli of comples convexity and makes a comparison with the more familiar modulus of uniform convexity. It is shown that unconditional convergence of implies convergence of . In the next section the moduli and are shown to be related. The method of proof gives rise to a theorem about strict c-convexity of Lp(X) and a result on the representability in Lp(X).

scholarly journals Uniform convexity of ψ-direct sums of Banach spaces

2003 ◽  
Vol 277 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Kichi-Suke Saito ◽  
Mikio Kato
Keyword(s):  
Banach Spaces ◽  
Uniform Convexity ◽  
Direct Sums

scholarly journals Some Aspects of Geometric Constants in Modular Spaces

2021 ◽  
Vol 1 (2) ◽  
pp. 151-163
Author(s):  
Zhijian Yang ◽  
Qi Liu ◽  
Muhammad Sarfraz ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Strict Convexity ◽  
Uniform Convexity ◽  
Normed Spaces ◽  
James Constant ◽  
Modular Spaces ◽  
The Relationship ◽  
Geometric Constants

In this paper, we generalize the typical geometric constants of Banach spaces to modular spaces. We study the equivalence between the convexity of modular and normed spaces, and obtain the relationship between ρ-Neumann-Jordan constant and ρ-James constant. In particular, we extend the convexity and smoothness modular, and obtain the criterion theorems of the uniform convexity and strict convexity.

Minimum selections and fixed points of set-valued operators in Banach spaces with some uniform convexity

2011 ◽  
Vol 217 (12) ◽  
pp. 6004-6010
Author(s):  
Xing-Hua Zhu ◽  
Jian-Zhong Xiao
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Uniform Convexity

scholarly journals Uniform convexity of Banach spaces l({p_{i}})

1971 ◽  
Vol 39 (3) ◽  
pp. 227-231 ◽  
Author(s):  
K. Sundaresan
Keyword(s):  
Banach Spaces ◽  
Uniform Convexity

scholarly journals The modulus of near smoothness of the lp product of a sequence of Banach spaces

1997 ◽  
Vol 39 (2) ◽  
pp. 153-165
Author(s):  
Leszek Olszowy
Keyword(s):  
Functional Analysis ◽  
Banach Spaces ◽  
Measure Of Noncompactness ◽  
Uniform Convexity ◽  
Uniform Smoothness ◽  
Classical Geometry ◽  
New Concepts

In the classical geometry of Banach spaces the notions of smoothness, uniform smoothness, strict and uniform convexity introduced by Day [1] and Clarkson [2] play a very important role and are used in many branches of functional analysis ([3,4,5], for example). In recent years a lot of papers have appeared containing interesting generalizations of these notions in terms of a measure of noncompactness. These new concepts investigated in this paper as near uniform smoothness, local near uniform smoothness and modulus of near smoothness have been introduced by Stachura and Sekowski [6] and Banaś [7] (see also [8,9]).

Complex Uniform Convexity and Riesz Measures

2004 ◽  
Vol 56 (2) ◽  
pp. 225-245 ◽  
Author(s):  
Gordon Blower ◽  
Thomas Ransford
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Mass Distribution ◽  
Complex Plane ◽  
Subharmonic Function ◽  
Uniform Convexity ◽  
Von Neumann ◽  
Riesz Measure

AbstractThe norm on a Banach space gives rise to a subharmonic function on the complex plane for which the distributional Laplacian gives a Riesz measure. This measure is calculated explicitly here for LebesgueLpspaces and the von Neumann-Schatten trace ideals. Banach spaces that areq-uniformly PL-convex in the sense of Davis, Garling and Tomczak-Jaegermann are characterized in terms of the mass distribution of this measure. This gives a new proof that the trace idealscpare 2-uniformly PL-convex for 1 ≤p≤ 2.

Operators which Factor through Convex Banach Lattices

1980 ◽  
Vol 32 (6) ◽  
pp. 1482-1500 ◽  
Author(s):  
Shlomo Reisner
Keyword(s):  
Banach Spaces ◽  
Banach Lattice ◽  
Interpolation Method ◽  
Banach Lattices ◽  
Uniform Convexity ◽  
Complex Interpolation ◽  
Power Type ◽  
Convex Operator ◽  
Image Position ◽  
The Ideal

We investigate here classes of operators T between Banach spaces E and F, which have factorization of the formwhere L is a Banach lattice, V is a p-convex operator, U is a q-concave operator (definitions below) and jF is the cannonical embedding of F in F”. We show that for fixed p, q this class forms a perfect normed ideal of operators Mp, q, generalizing the ideal Ip,q of [5]. We prove (Proposition 5) that Mp, q may be characterized by factorization through p-convex and q-concave Banach lattices. We use this fact together with a variant of the complex interpolation method introduced in [1], to show that an operator which belongs to Mp, q may be factored through a Banach lattice with modulus of uniform convexity (uniform smoothness) of power type arbitrarily close to q (to p). This last result yields similar geometric properties in subspaces of spaces having G.L. – l.u.st.

scholarly journals The fixed point property in banach spaces whose characteristic of uniform convexity is less than 2

1993 ◽  
Vol 54 (2) ◽  
pp. 169-173 ◽  
Author(s):  
J. García Falset
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Orthogonality Condition ◽  
Fixed Point Property ◽  
Uniform Convexity ◽  
Point Property

AbstractWe prove that every Banach space X with characteristic of uniform convexity less than 2 has the fixed point property whenever X satisfies a certain orthogonality condition.

On martingales with values in a complex Banach space

1988 ◽  
Vol 104 (2) ◽  
pp. 399-406 ◽  
Author(s):  
D. J. H. Garling
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Complex Banach Space ◽  
Uniform Convexity ◽  
Martingale Inequalities ◽  
Nikodym Property

In recent years it has become clear that there are several ways in which complex Banach spaces can differ quite markedly from their real counterparts, and many of these concern martingales. Thus, in [6] complex uniform convexity was related to martingale inequalities, in [3] and [7] the convergence of L1-bounded analytic martingales was considered and in [8] this property was related to the analytic Radon–Nikodym property.

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