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Some examples of continuous images of Radon-Nikodým compact spaces

Alexander D. Arvanitakis, Antonio Avilés (2009)

Czechoslovak Mathematical Journal

We provide a characterization of continuous images of Radon-Nikodým compacta lying in a product of real lines and model on it a method for constructing natural examples of such continuous images.

Some examples on quasi-barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled 𝒟 -space containing a subspace of infinite countable codimension which is not 𝒟 -space, and bornological barrelled space which is not inductive limit of Baire space.

Some generalization of Steinhaus' lattice points problem

Paweł Zwoleński (2011)

Colloquium Mathematicae

Steinhaus' lattice points problem addresses the question of whether it is possible to cover exactly n lattice points on the plane with an open ball for every fixed nonnegative integer n. This paper includes a theorem which can be used to solve the general problem of covering elements of so-called quasi-finite sets in Hilbert spaces. Some applications of this theorem are considered.

Some generalizations of Kadison's theorem: a survey.

T. S. S. R. K. Rao (2004)

Extracta Mathematicae

Motivated by a well-known result of Kadison that describes surjective isometries of the space of compact and the space of bounded operators on a Hilbert space, in this paper we investigate the structure of surjective isometries on the space of compact and on the space of bounded operators between Banach spaces. We give an example to show that isometries in general need not be of the canonical form. As an application of our study of the group of isometries, we consider the algebraic reflexivity of...

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