scholarly journals A Generalization of Uniformly Extremely Convex Banach Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Suyalatu Wulede ◽  
Wurichaihu Bai ◽  
Wurina Bao
Keyword(s):  
Banach Spaces ◽  
Uniformly Convex ◽  
Strongly Convex ◽  
New Class ◽  
Uniformly Convex Spaces ◽  
Convex Spaces

We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. We prove that the new class of Banach spaces lies strictly between either the classes ofk-uniformly rotund spaces andk-strongly convex spaces or classes of fullyk-convex spaces andk-strongly convex spaces and has no inclusive relation with the class of locallyk-uniformly convex spaces. We obtain in addition some characterizations and properties of this new class of Banach spaces. In particular, our results contain the main results of Wulede and Ha.

A new class of Banach space with the drop property

2012 ◽  
Vol 142 (1) ◽  
pp. 215-224 ◽  
Author(s):  
Suyalatu Wulede ◽  
Wudunqiqige Ha
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Uniformly Convex ◽  
Strongly Convex ◽  
New Class ◽  
Uniformly Convex Spaces ◽  
Convex Spaces

We discuss a new class of Banach spaces which are wider than the strongly convex spaces introduced by Congxin Wu and Yongjin Li. We prove that the new class of Banach spaces lies strictly between either the class of uniformly convex spaces and strongly convex spaces or the class of fully k-convex spaces and strongly convex spaces. The new class of Banach spaces has inclusive relations with neither the class of locally uniformly convex spaces nor the class of nearly uniformly convex spaces. We obtain in addition some characterizations of this new class of Banach spaces.

scholarly journals Embedding uniformly convex spaces into spaces with very few operators

2012 ◽  
Vol 262 (3) ◽  
pp. 825-849 ◽  
Author(s):  
S.A. Argyros ◽  
D. Freeman ◽  
R. Haydon ◽  
E. Odell ◽  
Th. Raikoftsalis ◽  
...  
Keyword(s):  
Uniformly Convex ◽  
Uniformly Convex Spaces ◽  
Convex Spaces

On nearly uniformly convex and k-uniformly convex spaces

1984 ◽  
Vol 95 (2) ◽  
pp. 325-327 ◽  
Author(s):  
V. I. Istrăt‚escu ◽  
J. R. Partington
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Normal Structure ◽  
Uniformly Convex ◽  
Uniformly Convex Space ◽  
Uniformly Convex Spaces ◽  
Convex Spaces

AbstractIn this note we prove that every nearly uniformly convex space has normal structure and that K-uniformly convex spaces are super-reflexive.We recall [1] that a Banach space is said to be Kadec–Klee if whenever xn → x weakly and ∥n∥ = ∥x∥ = 1 for all n then ∥xn −x∥ → 0. The stronger notions of nearly uniformly convex spaces and uniformly Kadec–Klee spaces were introduced by R. Huff in [1]. For the reader's convenience we recall them here.

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