Weak Convergence and Unconditionally Convergent Series in Uniformly Convex Spaces

1984 ◽  
pp. 124-146
Author(s):  
Joseph Diestel
Keyword(s):  
Weak Convergence ◽  
Convergent Series ◽  
Uniformly Convex ◽  
Unconditionally Convergent Series ◽  
Uniformly Convex Spaces ◽  
Convex 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.

scholarly journals Compactly uniformly convex spaces and property(β)of Rolewicz

2013 ◽  
Vol 402 (1) ◽  
pp. 297-307 ◽  
Author(s):  
S.J. Dilworth ◽  
Denka Kutzarova ◽  
N. Lovasoa Randrianarivony ◽  
J.P. Revalski ◽  
N.V. Zhivkov
Keyword(s):  
Uniformly Convex ◽  
Uniformly Convex Spaces ◽  
Convex Spaces

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.

Sign in / Sign up

Export Citation Format

Share Document