We show that when a linear quotient map to a separable Banach space X has a Lipschitz
right inverse, then it has a linear right inverse. If a separable space X embeds isometrically …

THE NON-LINEAR GEOMETRY OF BANACH SPACES AFTER NIGEL KALTON 1. Introduction.
Four articles among Nigel Kalton’s last papers ar Page 1 ROCKY MOUNTAIN JOURNAL OF …

It is no exaggeration to say that the theory of separably injective spaces is quite different
from that of injective spaces. In this chapter we will explain why. Indeed, we will enter now in …

Abstract top We describe how the Szlenk index has been used in various areas of the
geometry of Banach spaces. We cover the following domains of application of this notion …

We prove that the locally convex space $ C_ {p}(X) $ of continuous real-valued functions on
a Tychonoff space $ X $ equipped with the topology of pointwise convergence is …

We continue our initial study of C_ p (X) C p (X) spaces that are distinguished, equiv., are
large subspaces of R^ X RX, equiv., whose strong duals L_ β (X) L β (X) carry the strongest …

We show that there is no uniformly continuous selection of the quotient map Q: l∞→ l∞/c0
relative to the unit ball. We use this to construct an answer to a problem of Benyamini and …

In this article, we will focus on the interplay of weak topologies, smoothness and rotundity of
norms, biorthogonal systems and projectional resolutions of the identity operator in …

We deal with two weak forms of injectivity which turn out to have a rich structure behind:
separable injectivity and universal separable injectivity. We show several structural and …

Given a pseudocompact\varDelta Δ-space X, we establish that countable subsets of X must
be scattered. This implies that pseudocompact\varDelta Δ-spaces of countable tightness are …