WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Normal Structure, Slices and Other Properties in Banach Spaces
Authors: ,
Abstract: In this paper, we introduce parameters $$sl_{ε}(X)$$ and $$sl_{0}(X)$$ based on slices of Banach space $$X$$ Using these parameters we describe some new properties of Banach spaces related to normal structure, uniformly non-squareness and others. In particular, we prove that if $$sl _{\frac{2}{3}}(X) < 2$$, then $$X$$ has normal structure, and $$sl_{0}(X) = ε_{0}(X)$$ where $$ ε_{0}X$$ is the characteristic of convexity of $$X$$ In addition, we give much more results about the modulus of NUC on X, and the modulus of UKK∗ on the dual space X∗ of X.