On very rotund banach space

2000 ◽  
Vol 21 (8) ◽  
pp. 965-970 ◽  
Author(s):  
Zhang Zi-hou ◽  
Zhang Cong-jun
Keyword(s):  
Banach Space ◽  
Rotund Banach Space

scholarly journals A New Characterization ofk-Uniformly Rotund Banach Space

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Suyalatu Wulede ◽  
Tingting Li ◽  
Xuan Qin
Keyword(s):  
Banach Space ◽  
Rotund Banach Space

A new characterization ofk-uniformly rotund Banach space with1<P<+∞is given. Moreover, a corresponding result in the locallyk-uniformly rotund Banach space with1<P<+∞is given.

scholarly journals On strong proximinality in normed linear spaces

2016 ◽  
Vol 70 (1) ◽  
pp. 19
Author(s):  
Sahil Gupta ◽  
T. D. Narang
Keyword(s):  
Banach Space ◽  
Convex Sets ◽  
Linear Spaces ◽  
Quotient Spaces ◽  
Normed Linear Spaces ◽  
Rotund Banach Space ◽  
Approximative Compactness

The paper deals with strong proximinality in normed linear spaces. It is proved that in  a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and  approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed.

scholarly journals On the weak uniform rotundity of Banach spaces

2003 ◽  
Vol 2003 (30) ◽  
pp. 1943-1945
Author(s):  
Wen D. Chang ◽  
Ping Chang
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Product Space ◽  
Quotient Space ◽  
Uniform Rotundity ◽  
Rotund Banach Space

We prove that ifXi,i=1,2,…,are Banach spaces that are weak* uniformly rotund, then theirlpproduct space(p>1)is weak* uniformly rotund, and for any weak or weak* uniformly rotund Banach space, its quotient space is also weak or weak* uniformly rotund, respectively.

scholarly journals K-Uniform Rotundity of Sequence Orlicz Spaces

1991 ◽  
Vol 34 (1) ◽  
pp. 128-135 ◽  
Author(s):  
Wang Tingfu ◽  
Chen Shutao
Keyword(s):  
Banach Space ◽  
Orlicz Spaces ◽  
Uniform Rotundity ◽  
Rotund Banach Space

AbstractThis paper presents a criterion of KUR for sequence Orlicź spaces with Luxemburg's norm. The result also indicates that for any integer k ≥ 1, there exists a k + 1-uniformly rotund Banach space not being k-uniformly rotund.

scholarly journals Some questions about rotundity and renormings in Banach spaces

2005 ◽  
Vol 79 (1) ◽  
pp. 131-140 ◽  
Author(s):  
A. Aizpuru ◽  
F. J. Garcia-Pacheco
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Geometric Concepts ◽  
Strongly Exposed Points ◽  
Fréchet Differentiable ◽  
Rotund Banach Space

AbstractIn this paper, we show some results involving classical geometric concepts. For example, we characterize rotundity and Efimov-Stechkin property by mean of faces of the unit ball. Also, we prove that every almost locally uniformly rotund Banach space is locally uniformly rotund if its norm is Fréchet differentiable. Finally, we also provide some theorems in which we characterize the (strongly) exposed points of the unit ball using renormings.

scholarly journals Asplund spaces and a variant of weak uniform rotundity

2000 ◽  
Vol 61 (3) ◽  
pp. 451-454 ◽  
Author(s):  
John Giles ◽  
Jon Vanderwerff
Keyword(s):  
Banach Space ◽  
Asplund Space ◽  
Asplund Spaces ◽  
Uniform Rotundity ◽  
Rotund Norm ◽  
Rotund Banach Space

We introduce a property formally weaker than weak uniform rotundity, which we call equatorial weak uniform rotundity. We show that an equatorially weakly uniformly rotund norm need not be weakly locally uniformly rotund. Nevertheless, we show that an equatorially weakly uniformly rotund Banach space is an Asplund space.

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