Functional Analysis is devoted to the study of various structures that are defined on infinite-
dimensional linear spaces. Normed, Banach, and topological vector spaces, Hilbert spaces …

Most classes of operators that are not isomorphic embeddings are characterized by some
kind of a “smallness” condition. Narrow operators are those operators defined on function …

This is a commented collection of some easily formulated open problems in the geometry
and analysis on Banach spaces, focusing on basic linear geometry, convexity …

The computation of the numerical index of a Banach space is an intriguing problem, even in
case of two-dimensional real polyhedral Banach spaces. In this article we present a general …

We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for
short), which contains almost-CL-spaces, separable lush spaces (specially, separable $ C …

Let X and Y be Banach spaces. The main goal of this monograph is to study bounded linear
operators GW X! Y satisfying that for every other bounded linear operator TW X! Y there is a …

We introduce the class of slicely countably determined Banach spaces which contains in
particular all spaces with the Radon-Nikodým property and all spaces without copies of $\ell …

Given Banach spaces $ X $ and $ Y $, and a norm-one operator $ G\in\mathcal {L}(X, Y) $,
the numerical index with respect to $ G $, $ n_G (X, Y) $, is the greatest constant $ k\geq 0 …

The concept of lushness was introduced recently as a Banach space property, which
ensures that the space has numerical index 1. We prove that for Asplund spaces lushness is …

We give a lower bound for the numerical index of the real space L p (µ) showing, in
particular, that it is non-zero for p≠ 2. In other words, it is shown that for every bounded …