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Factorization of weakly continuous holomorphic mappings

Manuel González, Joaqín Gutiérrez (1996)

Studia Mathematica

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.

Lorenz Halbeisen (2005)

Extracta Mathematicae

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.

Fixed point free maps of a closed ball with small measures of noncompactness.

Martin Väth (2001)

Collectanea Mathematica

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 nonexpansive mappings in modular spaces

Poom Kumam (2004)

Archivum Mathematicum

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 ρ is a convex, ρ -complete modular space satisfying the Fatou property and ρ r -uniformly convex for all r > 0 , C a convex, ρ -closed, ρ -bounded subset of X ρ , T : C → C a ρ -nonexpansive mapping, then T has a fixed point.

Fixed points of asymptotically regular mappings in spaces with uniformly normal structure

Jarosław Górnicki (1991)

Commentationes Mathematicae Universitatis Carolinae

It is proved that: for every Banach space X which has uniformly normal structure there exists a k > 1 with the property: if A is a nonempty bounded closed convex subset of X and T : A → A is an asymptotically regular mapping such that lim inf n → ∞ | | | T n | | | < k , where | | | T | | | is the Lipschitz constant (norm) of T , then T has a fixed point in A .

Fragmentability and σ-fragmentability

J. Jayne, I. Namioka, C. Rogers (1993)

Fundamenta Mathematicae

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 ℓ ∞ and ℓ c ∞ ( Γ ) , with Γ uncountable, are determined.

Fragmentability of the Dual of a Banach Space with Smooth Bump

Kortezov, I. (1998)

Serdica Mathematical Journal

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.

Functions locally dependent on finitely many coordinates.

Petr Hájek, Václav Zizler (2006)

RACSAM

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.

Currently displaying 301 – 320 of 1093