Related papers: Generalized Drazin-meromorphic invertible operator…

We consider the Kato problem and extensions for degenerate elliptic operators of arbitrary order $2m$ ($m\geq 1$), whose coefficients are measurable, complex-valued and satisfy the G$\mathring{a}$rding inequality with respect to a…

In this paper, the author studies the boundedness for a large class of sublinear operator $T_\alpha, \alpha\in[0,n)$ generated by Calder{\'o}n-Zygmund operators ($\alpha=0$) and generated by fractional integral operator ($\alpha>0$) on…

Let $L= -\Delta+ V$ be a Schr\"odinger operator on $\mathbb R^d$, $d\geq 3$, where $V$ is a nonnegative potential, $V\ne 0$, and belongs to the reverse H\"older class $RH_{d/2}$. In this paper, we study the commutators $[b,T]$ for $T$ in a…

An operator $T$ from a Banach lattice $E$ into a Banach space is disjointly non-singular ($DN$-$S$, for short) if no restriction of $T$ to a subspace generated by a disjoint sequence is strictly singular. We obtain several results for…

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the invertible group $A^{-1}$ of a unital Banach algebra $A$ onto an open subgroup of the invertible group $B^{-1}$ of a unital Banach algebra $B$, then $T$ is…

We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with $4 \times 4$ matrix symbols. We discuss their norm, their kernel, Fredhomlness,…

For any measurable set $E$ of a measure space $(X, \mu)$, let $P_E$ be the (orthogonal) projection on the Hilbert space $L^2(X, \mu)$ with the range $ran \, P_E = \{f \in L^2(X, \mu) : f = 0 \ \ a.e. \ on \ E^c\}$ that is called a standard…

In this article, we establish some conditions for the boundedness of fractional integral operators on the vanishing generalized weighted Morrey spaces. We also investigate corresponding commutators generated by BMO functions.

We consider the commutators $[b,T]$ and $[b,I_{\rho}]$ on Orlicz-Morrey spaces, where $T$ is a Calder\'on-Zygmund operator, $I_{\rho}$ is a generalized fractional integral operator and $b$ is a function in generalized Campanato spaces. We…

In the present paper deals with asymptotical stability of Markov operators acting on abstract state spaces (i.e. an ordered Banach space, where the norm has an additivity property on the cone of positive elements). Basically, we are…

The problem involving the extension of functions from a certain class and defined on subdomains of the ambient space to the whole space is an old and a well investigated theme in analysis. A related question whether the extensions that…

Let $A\colon H\rightarrow H$ be a normal operator on an infinite-dimensional separable Hilbert space $H$ and let $S\subseteq H$ be a finite subset such that $\{A^nx\}_{n\geq 0,\,x\in S}$ can be rescaled to form a frame for $H$. That is,…

Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvents of linear pencils in Banach spaces. Some practical criterions for the existence of generalized…

In contrast to the classical complex spectral theory, where the spectrum is related to the invertibility of $\lambda-A:D(A)\subseteq X_\mathbb{C}\rightarrow X_\mathbb{C}$, in the noncommutative quaternionic $S$-spectral theory one uses the…

We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive…

For bounded Lebesgue measurable functions $f,g,\phi$ and $\psi$ on the unit circle, $P_{+}fP_{+}+P_{-}gP_{+} +P_{+}\phi P_{-}+P_{-}\psi P_{-}$ is called a generalized singular integral operator (GSIO) on $L^{2}(\mathbb{T})$, where $P_{+}$…

We obtain (i) a new, coordinate free, characterization of quasidiagonal operators with essential spectra contained in the unit circle by adapting the proof of a classical result in the theory of Banach spaces, (ii) an affirmative answer to…

We prove a new criterion of weak hypercyclicity of a bounded linear operator on a Banach space. Applying this criterion, we solve few open questions. Namely, we show that if $G$ is a region of $\C$ bounded by a smooth Jordan curve $\Gamma$…

Let $E$ and $G$ be two Banach function spaces, let $T \in \mathcal{L}(E,Y)$, and let ${\langle X,Y \rangle}$ be a Banach dual pair. In this paper we give conditions for which there exists a (necessarily unique) bounded linear operator…

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…