On a property of the norm which is close to local uniform rotundity

1985 ◽  
Vol 271 (2) ◽  
pp. 305-313 ◽  
Author(s):  
S. L. Troyanski
Keyword(s):  
Uniform Rotundity ◽  
Local Uniform Rotundity

scholarly journals Differentiability and local rotundity

1979 ◽  
Vol 28 (2) ◽  
pp. 205-213 ◽  
Author(s):  
A. C. Yorke
Keyword(s):  
Banach Space ◽  
Dense Subset ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Subject Classification ◽  
Uniform Rotundity ◽  
Fréchet Differentiable ◽  
Local Uniform Rotundity ◽  
Necessary And Sufficient ◽  
Nonreflexive Spaces

AbstractThe concept of very weak local uniform rotundity (very WLUR) is introduced. It is shown that if a Banach space E is WLUR, very WLUR, or LUR then its dual E* is smooth, very smooth, or Fréchet differentiable, respectively, on a norm dense subset. This leads to examples of nonreflexive spaces which are Fréchet differentiable at every nonzero point of a (relatively) norm dense subset of the embedding of E** in the fourth dual. When E is reflexive, necessary and sufficient conditions for E and E* to be WLUR and LUR are given.Subject classification (Amer. Math. Soc. (MOS) 1970): 46 B 99.

On Geometric Properties of Orlicz-Lorentz Spaces

1997 ◽  
Vol 40 (3) ◽  
pp. 316-329 ◽  
Author(s):  
H. Hudzik ◽  
A. Kamińska ◽  
M. Mastyło
Keyword(s):  
Lorentz Spaces ◽  
Luxemburg Norm ◽  
Geometric Properties ◽  
Uniform Rotundity ◽  
Local Uniform Rotundity

AbstractCriteria for local uniform rotundity and midpoint local uniform rotundity in Orlicz-Lorentz spaces with the Luxemburg norm are given. Strict K-monotonicity and Kadec-Klee property are also discussed.

scholarly journals Strongly normal cones and the midpoint locally uniform rotundity

Positivity ◽  
2012 ◽  
Vol 17 (3) ◽  
pp. 935-940 ◽  
Author(s):  
K. V. Storozhuk
Keyword(s):  
Normal Cones ◽  
Uniform Rotundity
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