Familles absolument sommables et propriété de Radon-Nikodym
First results on spectrally bounded operators
A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ Mr(x) for all x ∈ E, where r(·) denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.
Fixed point theorems in cone Banach spaces.
Fragmentable mappings and CHART groups
The purpose of this note is two-fold: firstly, to give a new and interesting result concerning separate and joint continuity, and secondly, to give a stream-lined (and self-contained) proof of the fact that "tame" CHART groups are topological groups.
Fréchet differentiability of Lipschitz functions via a variational principle
Fredholm random operators and random subspaces in Banach spaces
General convexity of some functionals in seminormed spaces and seminormed algebras.
Generalizations of the Lax-Milgram theorem.
Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces
In this paper we deal with weakly upper semi-continuous set-valued maps, taking arbitrary non-empty values, from a non-metric domain to a Banach space. We obtain selectors having the point of continuity property relative to the norm topology for a large class of compact spaces as a domain. Exact conditions under which the selector is of the first Borel class are also investigated.
Generalized induced norms
Let be a norm on the algebra of all matrices over . An interesting problem in matrix theory is that “Are there two norms and on such that for all ?” We will investigate this problem and its various aspects and will discuss some conditions under which .
Generalized modular spaces
Geometric characterizations of the Radon-Nikodym property in Banach spaces
Geometry of Banach spaces and biorthogonal systems
A separable Banach space X contains isomorphically if and only if X has a bounded fundamental total -stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total -biorthogonal system.
Group representations in non-archimedean Banach spaces
Higher order differentiability of nonlinear operators on normed spaces. II.
Higher-Order Partial Differentiation
In this article, we shall extend the formalization of [10] to discuss higher-order partial differentiation of real valued functions. The linearity of this operator is also proved (refer to [10], [12] and [13] for partial differentiation).
Holomorphic germs on Banach spaces
Let and be two complex Banach spaces, a nonempty subset of and a compact subset of . The concept of holomorphy type between and , and the natural locally convex topology on the vector space of all holomorphic mappings of a given holomorphy type from to were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space of all germs of holomorphic mappings into around of a given holomorphy type , and study its interplay with and some...
Hopf Extension Theorem of Measure
The authors have presented some articles about Lebesgue type integration theory. In our previous articles [12, 13, 26], we assumed that some σ-additive measure existed and that a function was measurable on that measure. However the existence of such a measure is not trivial. In general, because the construction of a finite additive measure is comparatively easy, to induce a σ-additive measure a finite additive measure is used. This is known as an E. Hopf's extension theorem of measure [15].
Infinite Dimensional Polytopes.
Infinitely divisible probability measures and the converse Kolmogorov inequality in Banach spaces