相关论文: Multipliers and operator space structure of weak p…

In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of…

The aim of this article is to give a complete solution to the problem of the bilinear decompositions of the products of some Hardy spaces $H^p(\mathbb{R}^n)$ and their duals in the case when $p<1$ and near to $1$, via wavelets, paraproducts…

We study the quasi-nilpotency of generalized Volterra operators on spaces of power series with Taylor coefficients in weighted $\ell^p$ spaces $1<p<+\infty$ . Our main result is that when an analytic symbol $g$ is a multiplier for a…

Let $G$ be a finite pseudoreflection group, $\Omega\subseteq \mathbb C^n$ be a bounded domain which is a $G$-space and $\mathcal H\subseteq\mathcal O(\Omega)$ be an analytic Hilbert module possessing a $G$-invariant reproducing kernel. We…

Let $H$ be a Hilbert space of entire functions. Let $H'$ be the space of the functions $f(z)/\prod_i(z-z_i)$ where $f$ belongs to $H$ and vanishes at $n$ given complex points $z_i$. We compute a suitable $E$ function for $H'$ when one is…

We construct a weak Hilbert Banach space such that for every block subspace $Y$ every bounded linear operator on Y is of the form D+S where S is a strictly singular operator and D is a diagonal operator. We show that this yields a weak…

It is well known that on the Hardy space $H^2(\mathbb{D})$ or weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ over the unit disk, the adjoint of a linear fractional composition operator equals the product of a composition operator and two…

Let $p\in(0, 1]$. In this paper, the authors prove that a sublinear operator $T$ (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spaces $H^p({{\mathbb…

In the paper compact multiplier operators on Banach spaces of analytic functions on the unit disk with the range in Banach sequence lattices are studied. If the domain space $X$ is such that $H_\infty\hookrightarrow X\hookrightarrow H_1$,…

In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a…

We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…

We establish new Calder\'{o}n reproducing formulas for self-adjoint operators $D$ that generate strongly continuous groups with finite propagation speed. These formulas allow the analysing function to interact with $D$ through holomorphic…

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the operator $[V_1\...\ V_n]:H^n\to H$ is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the…

Let H and K be infinite dimensional Hilbert spaces, while B(H) and B(K) denote the algebras of all linear bounded operators on H and K, respectively. We characterize the forms of additive mappings from B(H) into B(K) that preserve the…

Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…

We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…

Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n-times weakly D-differentiable, if for any pair of vectors a, b from H the function < exp(itD)x exp(-itD) a, b> is n-times…

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, the authors introduce the weak Hardy-type space $WH_X({\mathbb R}^n)$, associated with $X$, via the radial maximal function. Assuming that the powered…

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group $G$ and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space $\mathcal{B}(L^2(G))$…