Related papers: Closed range of generalized integration operators …

We introduce the notion of a g-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of g-fusion frames. Also we shall describe the concept of…

In this article, we develop an algorithm to calculate the set of all integers $m$ for which there exists a linear operator $T$ on ${\mathbb R}^n$ such that ${\mathbb R}^n$ has exactly $m$ $T$-invariant subspaces. A brief discussion is…

In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1.…

Generalized fusion frame and some of their properties in tensor product of Hilbert spaces are described. Also, the canonical dual g-fusion frame in tensor product of Hilbert spaces is considered. Finally, the frame operator for a pair of…

The paper aims to provide a full characterization of all operators $T\colon \mathscr{P}(\mathbb{C}) \to \mathscr{P}(\mathbb{C})$ acting on the space of all complex polynomials that satisfy the Leibniz rule \[ T(f\cdot g)= T(f)\cdot g+f\cdot…

Necessary and sufficient conditions for positive Toeplitz operators on the Bergman space of a minimal bounded homogeneous domain to be bounded or compact are described in terms of the Berezin transform, the averaging function and the…

We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…

We study tent spaces on general measure spaces $(\Omega, \mu)$. We assume that there exists a semigroup of positive operators on $L^p(\Omega, \mu)$ satisfying a monotone property but do not assume any geometric/metric structure on $\Omega$.…

We study operators of the form $$ Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt, $$ where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$…

In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…

We prove that strictly elliptic operators with generalized Wentzell boundary conditions generate analytic semigroups of angle $\frac{\pi}{2}$ on the space of continuous function on a compact manifold with boundary.

We introduce generalised weighted central Morrey spaces over local fields and obtain a quantitative estimate for the boundedness of the Hardy--Hilbert-type integral operator on these newly introduced spaces, albeit specifically in the…

This work addresses the resolvent convergence of generalized MIT bag operators to Dirac operators with zigzag type boundary conditions. We prove that the convergence holds in strong but not in norm resolvent sense. Moreover, we show that…

In this paper we will give necessary and sufficient conditions for the operator $T_\nu^s$ to be in the symmetrically normed ideal $\mathcal{C}_\Phi$ for an arbitrary symmetric norming function $\Phi$ where $T_\nu$ is the Toeplitz operator…

We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund type spaces. Consequently, we obtain new characterizations for the compactness of such…

Let ${\bf R}$ denote any of the following classes: upper (lower) semi-Fredholm operators, Fredholm operators, upper (lower) semi-Weyl operators, Weyl operators, upper (lower) semi-Browder operators, Browder operators. For a bounded linear…

We give sufficient conditions on an operator space $E$ and on a semigroup of operators on a von Neumann algebra $M$ to obtain a bounded analytic or a $R$-analytic semigroup $(T_t \otimes Id_E)_{t \geq 0}$ on the vector valued noncommutative…

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.…

Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…

This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are…