An essential part of the work is devoted to the study of the sets of Fréchet subdi erentiability from the view of the descriptive set theory. Proofs of the known results of L. Zajíek, P. Holický, M. Laczkovich and M. Šmídek are given. A new result is that there exists a Lipschitz function with non-Borel set of Fréchet subdi erentiability on every non-reflexive Banach space. The Borel classes of the sets of Fréchet subdi erentiability of continuous functions on reflexive spaces are studied as well. Further, some sets of sequences in Banach spaces are investigated. A modi ed proof of the theorem of R. Kaufman which says that every non-re exive Banach space can be renormed not to have Borel set of norm-attaining functionals is shown. A charact...
. Various properties of Banach spaces, including the reflexivity and the Schur property of a space, ...
In this note, we prove a characterization of reexive Banach spaces with unconditional basis and stud...
AbstractIt is shown that a Banach space X is not superreflexive iff there exists a Banach space Y, f...
The thesis consists of three papers of the author. In the first paper, it is shown that the sets of ...
The thesis consists of three papers of the author. In the first paper, it is shown that the sets of ...
ABSTRACT. As a consequence of results due to Bourgain and Stegall, on a separable Banach space whose...
Two properties concerning the space of differences of sublinear functions D(X) for a real Banach spa...
Cette thèse traite de la théorie descriptive des ensembles et de la géométrie des espaces de Banach....
Cette thèse traite de la théorie descriptive des ensembles et de la géométrie des espaces de Banach....
AbstractIt is known that the Banach space BV of functions of bounded variation on a closed interval ...
Dedicated to the memory of Prof. Klaus Floret. Abstract. We prove that a Banach space that is convex...
summary:Let $f$ be a Lipschitz function on a superreflexive Banach space $X$. We prove that then the...
This book makes a significant inroad into the unexpectedly difficult question of existence of Frchet...
The purpose of this paper is to study certain geometrical properties for non-complete normed spaces....
In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's...
. Various properties of Banach spaces, including the reflexivity and the Schur property of a space, ...
In this note, we prove a characterization of reexive Banach spaces with unconditional basis and stud...
AbstractIt is shown that a Banach space X is not superreflexive iff there exists a Banach space Y, f...
The thesis consists of three papers of the author. In the first paper, it is shown that the sets of ...
The thesis consists of three papers of the author. In the first paper, it is shown that the sets of ...
ABSTRACT. As a consequence of results due to Bourgain and Stegall, on a separable Banach space whose...
Two properties concerning the space of differences of sublinear functions D(X) for a real Banach spa...
Cette thèse traite de la théorie descriptive des ensembles et de la géométrie des espaces de Banach....
Cette thèse traite de la théorie descriptive des ensembles et de la géométrie des espaces de Banach....
AbstractIt is known that the Banach space BV of functions of bounded variation on a closed interval ...
Dedicated to the memory of Prof. Klaus Floret. Abstract. We prove that a Banach space that is convex...
summary:Let $f$ be a Lipschitz function on a superreflexive Banach space $X$. We prove that then the...
This book makes a significant inroad into the unexpectedly difficult question of existence of Frchet...
The purpose of this paper is to study certain geometrical properties for non-complete normed spaces....
In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's...
. Various properties of Banach spaces, including the reflexivity and the Schur property of a space, ...
In this note, we prove a characterization of reexive Banach spaces with unconditional basis and stud...
AbstractIt is shown that a Banach space X is not superreflexive iff there exists a Banach space Y, f...
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