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A note on intermediate differentiability of Lipschitz functions

Luděk Zajíček (1999)

Commentationes Mathematicae Universitatis Carolinae

Let f be a Lipschitz function on a superreflexive Banach space X . We prove that then the set of points of X at which f has no intermediate derivative is not only a first category set (which was proved by M. Fabian and D. Preiss for much more general spaces X ), but it is even σ -porous in a rather strong sense. In fact, we prove the result even for a stronger notion of uniform intermediate derivative which was defined by J.R. Giles and S. Sciffer.

A note on intersections of simplices

David A. Edwards, Ondřej F. K. Kalenda, Jiří Spurný (2011)

Bulletin de la Société Mathématique de France

We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.

A note on lattice renormings

Marián J. Fabián, Petr Hájek, Václav Zizler (1997)

Commentationes Mathematicae Universitatis Carolinae

It is shown that every strongly lattice norm on c 0 ( Γ ) can be approximated by C ∞ smooth norms. We also show that there is no lattice and Gâteaux differentiable norm on C 0 [ 0 , ω 1 ] .

A note on L-Dunford-Pettis sets in a topological dual Banach space

Abderrahman Retbi (2020)

Czechoslovak Mathematical Journal

The present paper is devoted to some applications of the notion of L-Dunford-Pettis sets to several classes of operators on Banach lattices. More precisely, we establish some characterizations of weak Dunford-Pettis, Dunford-Pettis completely continuous, and weak almost Dunford-Pettis operators. Next, we study the relationships between L-Dunford-Pettis, and Dunford-Pettis (relatively compact) sets in topological dual Banach spaces.

A note on Lipschitz isomorphisms in Hilbert spaces

Dean Ives (2010)

Commentationes Mathematicae Universitatis Carolinae

We show that the following well-known open problems on existence of Lipschitz isomorphisms between subsets of Hilbert spaces are equivalent: Are balls isomorphic to spheres? Is the whole space isomorphic to the half space?

A note on local automorphisms

Ajda Fošner (2006)

Czechoslovak Mathematical Journal

Let H be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of ℬ ( H ) , the algebra of all bounded linear operators on a Hilbert space H , is an automorphism.

A Note on L-sets

Gero Fendler (2002)

Colloquium Mathematicae

Answering a question of Pisier, posed in [10], we construct an L-set which is not a finite union of translates of free sets.

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