Factoring unconditionally converging operators
Factorisation des propriétés de Banach-Saks
Factorisation d'opérateurs aléatoires, d'après Benyamini et Gordon
Factorization of compact operators and finite representability of Banach spaces with applications to Schwartz spaces
Factorization of weakly continuous holomorphic mappings
We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser...
Families of almost disjoint Hamel bases.
For infinite dimensional Banach spaces X we investigate the maximal size of a family of pairwise almost disjoint normalized Hamel bases of X, where two sets A and B are said to be almost disjoint if the cardinality of A ∩ B is smaller than the cardinality of either A or B.
Farthest points and subdifferential in -normed spaces.
Finite dimensional projection constants
Finite-dimensional Banach spaces with numerical index zero.
Finite-dimensional Banach spaces with symmetry constant of order √n
Fixed point free maps of a closed ball with small measures of noncompactness.
We show that in all infinite-dimensional normed spaces it is possible to construct a fixed point free continuous map of the unit ball whose measure of noncompactness is bounded by 2. Moreover, for a large class of spaces (containing separable spaces, Hilbert spaces and l-infinity (S)) even the best possible bound 1 is attained for certain measures of noncompactness.
Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces.
Fixed point theorems for nonexpansive mappings in modular spaces
In this paper, we extend several concepts from geometry of Banach spaces to modular spaces. With a careful generalization, we can cover all corresponding results in the former setting. Main result we prove says that if is a convex, -complete modular space satisfying the Fatou property and -uniformly convex for all , C a convex, -closed, -bounded subset of , a -nonexpansive mapping, then has a fixed point.
Fixed points of asymptotically regular mappings in spaces with uniformly normal structure
It is proved that: for every Banach space which has uniformly normal structure there exists a with the property: if is a nonempty bounded closed convex subset of and is an asymptotically regular mapping such that where is the Lipschitz constant (norm) of , then has a fixed point in .
Flat spaces of continuous functions
Fragmentability and σ-fragmentability
Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces and , with Γ uncountable, are determined.
Fragmentability of the Dual of a Banach Space with Smooth Bump
We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.
From finite- to infinite-dimensional phenomena in geometric functional analysis on local and asymptotic levels.
Functions locally dependent on finitely many coordinates.
The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher smoothness (C∞) is involved. In this note we survey most of the main results in this area, and indicate many old as well as new open problems.
Further properties of Azimi-Hagler Banach spaces