Related papers: A Superclass of the Posinormal Operators
In this paper, we establish the essential criteria for the hyponormality and quasinormality of the unbounded Toeplitz operator $T_{\varphi}$ with non-harmonic symbol, acting on the Fock-Sobolev space $F^{2, m}(\mathbb{C})$. The study shows…
We characterize disjoint hypercyclic sequences of wedge operators. Also, we give some sufficient conditions for a sequence of the dual wedge operators to be disjoint topologically transitive. Finally, we give some concrete examples and…
It is proved that for every stratifiable space $Y$ and a closed subset $X\subset Y$ there exists a regular (i.e. linear positive with unit norm) extension operator $T:C(X\times X)\to C(Y\times Y)$ preserving the class of (pseudo)metrics.…
We introduce a new class of fully nonlinear integro-differential operators with possible nonsymmetric kernels, which includes the ones that arise from stochastic control problems with purely jump L\`evy processes. If the index of the…
This paper investigates the algebraic properties of the hyperinterpolation class $\mathbf{HC}(\mathbb{S}^d)$ on the unit sphere $ \mathbb{S}^d $. We focus on operators derived from the classical hyperinterpolation with bounded $ L_2 $…
In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some…
We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint…
In [10], the authors formalized the standard transformation procedure for prenex normalization of first-order formulas and showed that the classes $\mathrm{E}_k$ and $\mathrm{U}_k$ introduced in Akama et al. [1] are exactly the classes…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
This paper introduces the seed order, a partial order of the class of uniform countably complete ultrafilters that generalizes the Mitchell order on normal measures. Like that order, the seed order is consistently a linear ordering even…
In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We…
By means of a fixed point method we discuss the deformation of operator means and multivariate means of positive definite matrices/operators. It is shown that the deformation of an operator mean becomes again an operator mean. The means…
Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on…
In this paper, we describe necessary and sufficient conditions for a binormal or complex symmetric operator to have the other property. Along the way, we find connections to the Duggal and Aluthge transforms, and give further properties of…
The purpose of this paper is to obtain microlocal analogues of results by L. H \"ormander about inclusion relations between the ranges of first order differential operators with coefficients in $C^\infty$ which fail to be locally solvable.…
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential…
We prove the subnormality of an operator-weighted composition operator whose symbol is a transformation of a discrete measure space and weights are multiplication operators in $L^2$-spaces under the assumption of existence of a family of…
This study is an attempt at generalizing the class of partially hypoelliptic differential operators to a class of pseudodifferential operators, Symbol ideals are formed on the set of lineality and we discuss suitable topologies that allow…
Given a Furstenberg family F and a subset {\Gamma} of C, we introduce and explore the notions of F_{\Gamma}-hypercyclic operator and F-hypercyclic scalar set. First, the study of F_C-hypercyclic operators yields new interesting information…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…