Related papers: Operateurs absolument continus et interpolation

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

In this paper we introduce and study absolute continuity and singularity of positive operators acting on anti-dual pairs. We establish a general theorem that can be considered as a common generalization of various earlier Lebesgue-type…

We study the interpolation and extrapolation properties of strictly singular operators between different $L_p$ spaces. To this end, the structure of strictly singular non-compact operators between $L_p-L_q$ spaces is analyzed. Among other…

In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…

This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective…

Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…

In [1], an operator was introduced which acts parallel to the Riemann-Liouville differintegral on a transformation of the space of real analytic functions and commutes with itself. This paper aims to extend the technique - and its defining…

We consider a general schema involving measure spaces, contractions and linear and continuous operators. Within the framework of this schema we use our sesquilinear uniform integral and introduce some integral operators on continuous vector…

Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

In this paper we introduce two new classes of operators that we call strongly order continuous and strongly $\sigma$-order continuous operators. An operator $T:E\rightarrow F$ between two Riesz spaces is said to be strongly order continuous…

We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

Let $H$ be an infinite dimensional Hilbert space. We show that there exists a subspace of $B(H)$ which is isometric to $\ell_2$ and completely isometric to its antidual in the sense of the theory of operator spaces recently developed by…

We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…

In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a band. In addition, we look into some situations under which,…

We conclude the classification of spaces of continuous functions on ordinals carried out by R. Gorak. This gives a complete topological classification of the spaces $C_p([0,\alpha])$ of all continuous real-valued functions on compact…

We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…

In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of complementability in the sense of Ando for operators, and study the…

We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…

In this paper we study some questions about the continuity of classical and fractional maximal operators in the Sobolev space $W^{1,1}$, in both continuous and discrete setting, giving a positive answer to two questions posed recently, one…