We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of H...

An important problem in topology is to determine the effects on the function space of imposing some natural topological condition on the space X [5]. In this way, it is practical to characterize the complemented subalgebras of Banach algebras. In our investigation, we relate the second category property of [0,1] with certain properties of the complemented subalgebras of bounded real Baire-1 fun...

We prove that for all 1 ≤ p ≤ ∞, p 6= 2, the Lp spaces associated to two von Neumann algebrasM, N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative Lp Banach-Stone theorem: a specific decomposition for surjective isometries of noncommutative Lp spaces.

We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following: let X be a Banach space with an unconditional basis {ei}i∈N; then either there exists a perfect set P of infinite subsets of N such that for any two distinct A,B ∈ P, [ei]i∈A ≇ [ei]i∈B , or for a residual set of infinite subsets A of N, [ei]i∈A is isomorphic to X, and in that case, X is is...

We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following: let X be a Banach space with an unconditional basis {ei}i∈N; then either there exists a perfect set P of infinite subsets of N such that for any two distinct A,B ∈ P, [ei]i∈A ≇ [ei]i∈B , or for a residual set of infinite subsets A of N, [ei]i∈A is isomorphic to X, and in that case, X is is...