scholarly journals A NEW CHARACTERIZATION OF REFLEXIVITY

2008 ◽  
Vol 78 (3) ◽  
pp. 443-444
Author(s):  
RUIDONG WANG
Keyword(s):  
Banach Spaces ◽  
Convex Sets ◽  
Reflexive Banach Spaces ◽  
Bounded Convex

AbstractIn this paper, we give a new characterization of reflexive Banach spaces in terms of the sum of two closed bounded convex sets.

scholarly journals A Characterization of Polynomially Convex Sets in Banach Spaces

2017 ◽  
Vol 72 (4) ◽  
pp. 2013-2021
Author(s):  
Mortaza Abtahi ◽  
Sara Farhangi
Keyword(s):  
Banach Spaces ◽  
Convex Sets ◽  
Polynomially Convex

A characterization of essentially strictly convex functions on reflexive Banach spaces

2012 ◽  
Vol 75 (3) ◽  
pp. 1617-1622 ◽  
Author(s):  
Michel Volle ◽  
Jean-Baptiste Hiriart-Urruty
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Reflexive Banach Spaces ◽  
Strictly Convex

On Super Weakly Compact Convex Sets and Representation of the Dual of the Normed Semigroup They Generate

2013 ◽  
Vol 56 (2) ◽  
pp. 272-282 ◽  
Author(s):  
Lixin Cheng ◽  
Zhenghua Luo ◽  
Yu Zhou
Keyword(s):  
Banach Space ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Lower Semicontinuous ◽  
Weakly Compact ◽  
Bounded Set ◽  
Fréchet Differentiable ◽  
Bounded Convex

AbstractIn this note, we first give a characterization of super weakly compact convex sets of a Banach space X: a closed bounded convex set K ⊂ X is super weakly compact if and only if there exists a w* lower semicontinuous seminorm p with p ≥ σK ≌ supxєK 〈.,x〉 such that p2 is uniformly Fréchet differentiable on each bounded set of X*. Then we present a representation theoremfor the dual of the semigroup swcc(X) consisting of all the nonempty super weakly compact convex sets of the space X.

scholarly journals Characterization of Reflexivity by Convex Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-4
Author(s):  
Zhenghua Luo ◽  
Qingjin Cheng
Keyword(s):  
Banach Spaces ◽  
Convex Functions ◽  
Convexity Property ◽  
Reflexive Banach Spaces

A new convexity property of convex functions is introduced. This property provides, in particular, a characterization of the class of reflexive Banach spaces.

scholarly journals A characterization of reflexive Banach spaces

1996 ◽  
Vol 124 (4) ◽  
pp. 1083-1090 ◽  
Author(s):  
Eva Matoušková ◽  
Charles Stegall
Keyword(s):  
Banach Spaces ◽  
Reflexive Banach Spaces
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