Some geometric inequalities for the Holmes-Thompson definitions of volume and surface area in Minkowski spaces.
Some geometric properties concerning fixed point theory.
The Fixed Point Theory for nonexpansive mappings is strongly based upon the geometry of the ambient Banach space. In section 1 we state the role which is played by the multidimensional convexity and smoothness in this theory. In section 2 we study the computation of the normal structure coefficient in finite dimensional lp-spaces and its connection with several classic geometric problems.
Some geometric properties in Orlicz sequence spaces equipped with Orlicz norm.
Some geometric properties of a generalized Cesàro sequence space.
Some geometric properties of finite dimensional, symmetric Banach spaces
Some geometric properties related to fixed point theory in Cesàro spaces.
Some inequalities concerning the weakly convergent sequence coefficient in Banach spaces.
Some isomorphic properties in projective tensor products
We give sufficient conditions implying that the projective tensor product of two Banach spaces and has the -sequentially Right and the --limited properties, .
Some modulus and normal structure in Banach space.
Some more weak Hubert spaces
We construct, by a variation of the method used to construct the Tsirelson spaces, a new family of weak Hilbert spaces which contain copies of l₂ inside every subspace.
Some natural families of M-ideals.
Some new results on accretive multivalued operators
Some notes about the convexity module.
Some permanence results of properties of Banach spaces
Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.
Some properties of -convexity.
Some properties of Pythagorean modulus.
Some properties of weakly countably determined Banach spaces
Some properties on the closed subsets in Banach spaces
It is shown that under natural assumptions, there exists a linear functional does not have supremum on a closed bounded subset. That is the James Theorem for non-convex bodies. Also, a non-linear version of the Bishop-Phelps Theorem and a geometrical version of the formula of the subdifferential of the sum of two functions are obtained.
Some Ramsey type theorems for normed and quasinormed spaces
We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.
Some recent results concerning weak Asplund spaces