Topological balls
Topological proper separation theorems
Two mappings related to semi-inner products and their applications in geometry of normed linear spaces
In this paper we introduce two mappings associated with the lower and upper semi-inner product and and with semi-inner products (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants.
Two remarks on the Khintchine-Kahane inequality
Typical sets and typical continuous functions
Über den Zusammenhang von schlichten Funktionen im Banachraum B.
Über die Cunningham-oo-Algebra und den Zentralisator reeller Banachräume.
Über Differentialgleichungen in n. a. Banachräumen, insbesondere ihre Lösung mittels eines ,, Wegintegrales".
Über homöomorphe und differenzierbare Abbildungen N.A. Banachräume.
U-ideals of factorable operators
We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons’s construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are -ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.
Ultraproducts in Banach space theory.
Ultraproduits d'espaces de Banach
Ultraproduits d’espaces et d’espaces d’Orlicz
Un altro modo di costruire la serie di Fourier delle distribuzioni di una variabile quasi periodiche
Un théorème d’extrapolation et son application aux suites sommables dans
Uncomplementability of spaces of compact operators in larger spaces of operators
In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results...
Une classe d'espaces de Banach réticulés.
Une propriété du type -stable
Une remarque sur les espaces de Banach mesure-compacts
Uniform maps into normed spaces
Thirteen properties of uniform spaces are shown to be equivalent. The most important properties seem to be those related to modules of uniformly continuous mappings into normed spaces, and to partitions of unity.