We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.
Motivated by a well-known result of Kadison that describes surjective isometries of the space of compact and the space of bounded operators on a Hilbert space, in this paper we investigate the structure of surjective isometries on the space of compact and on the space of bounded operators between Banach spaces. We give an example to show that isometries in general need not be of the canonical form. As an application of our study of the group of isometries, we consider the algebraic reflexivity of...
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.
We give sufficient conditions implying that the projective tensor product of two Banach spaces and has the -sequentially Right and the --limited properties, .