相关论文: Banach space valued mean periodic functions
Necessary and sufficient conditions for a separable Banach space to be a dual space are proved. Some applications are discussed
We are interested in a sufficient condition given in an article by P. Lef\`evre, \'E. Matheron and A. Primot to obtain the Blum-Hanson Property and we then partially answer two questions asked in this same article on other possible…
In this paper, we give necessary and sufficient conditions for the space B_1(X) of first Baire class functions on a Tychonoff space X, with pointwise topology, to be (strongly) sequentially separable.
We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a…
In this paper we give necessary and sufficient conditions for the norm on an infinite dimensional Banach space to be sub differentiable, for various classes of Bananch spaces.
We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism.
We show that if $X$ and $Y$ are Banach spaces, where $Y$ is separable and polyhedral, and if $T:X \to Y$ is a bounded linear operator such that $T^*(Y^*)$ contains a boundary $B$ of $X$, then $X$ is separable and isomorphic to a polyhedral…
Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.
We will show that Banach spaces are monadic over complete metric spaces via the unit ball functor. For the forgetful functor, one should take complete pointed metric spaces.
We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.
This paper presents a necessary and sufficient condition for a real-valued function defined on an open and convex subset of a Banach space to be quasi-concave, and a sufficient condition for such a function to be strictly quasi-concave.…
Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.
We construct Zachary space in $\R^\infty$ and find that this is a Banach space of functions of bounded mean oscillation with order $p, 1\leq p \leq \infty$ containing the function of bounded mean oscillation $BMO[\R_I^\infty]$ as a dense…
The main aim of this note is to introduce the notion of an almost anti-periodic function in Banach space. We prove some characterizations for this class of functions, investigating also its relationship with the classes of anti-periodic…
Solutions of some partial differential equations are obtained as critical points of a real funtional. Then the Banach space where this functional is defined has to be real, otherwise, it is not differentiable. It follows that the equation…
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…
The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…
We consider weighted banach spaces of holomorphic functions on the upper half plane that are determined by $ \|f\|=\sup_{y>0,-\infty<x<\infty}p(y)|f(x+iy)|<\infty $ for a very large class of weight functions p. We completely solve the…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
The notion of adequate function has been recently introduced in order to characterize the essentially strictly functions on a reflexive Banach space among the weakly lower semicontinuous ones. In this paper we reinforce this concept and…