Banach spaces provide a framework for modern mathematical analysis, as they blend
classical analysis, geometry, topology and linearity. This makes Banach space theory a …

Let be a Banach space with a fundamental biorthogonal system, and let be the dense
subspace spanned by the vectors of the system. We prove that admits a-smooth norm that …

We provide, in every infinite-dimensional separable Banach space, an average locally
uniformly rotund (and hence rotund) Gâteaux smooth renorming which is not locally …

SMOOTH APPROXIMATIONS OF NORMS IN SEPARABLE BANACH SPACES Page 1 The
Quarterly Journal of Mathematics Advance Access published on December 12, 2013 Quart. J …

We show that norms on certain Banach spaces X can be approximated uniformly, and with
arbitrary precision, on bounded subsets of X by C∞ smooth norms and polyhedral norms. In …

We prove that in every separable Banach space X with a Schauder basis and a C k-smooth
norm it is possible to approximate, uniformly on bounded sets, every equivalent norm with a …

This chapter—that has a survey character—contains a collection of problems in analysis and
geometry of Banach spaces followed by some others from operator theory. It claims to show …

The main line of investigation of the present work is the study of some aspects in the
analysis of the structure of the unit ball of (infinite-dimensional) Banach spaces. In particular …

Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on c 0
(Γ) can be approximated uniformly on bounded sets by polyhedral norms and C∞ smooth …

We further develop a classical geometric construction of V. Klee and show, typically, that if X
is a nonreflexive Banach space with separable dual, then X admits an equivalent norm|⋅ …