Related papers: Commutativity up to a factor for bounded and unbou…

We study the solvability of boundary-value problems for differential-operator equations of the second order in L p (0, 1; X), with 1 < p < +$\infty$, X being a UMD complex Banach space. The originality of this work lies in the fact that we…

We consider in a Hilbert space a self-adjoint operator H and a family Phi=(Phi_1,...,Phi_d) of mutually commuting self-adjoint operators. Under some regularity properties of H with respect to Phi, we propose two new formulae for a time…

Commutator relations are used to investigate the spectra of Schr\"odinger Hamiltonians, $H = -\Delta + V({x}),$ acting on functions of a smooth, compact $d$-dimensional manifold $M$ immersed in $\bbr^{\nu}, \nu \geq d+1$. Here $\Delta$…

We study the problem when an almost commuting $n$-tuple self-adjoint operators in an infinite dimensional separable Hilbert space $H$ is close to an $n$-tuple of commuting self-adjoint operators on $H.$ We give an affirmative answer to the…

We investigate some bounded linear operators T on a Hilbert space which satisfy the condition |T | less or equal to |ReT |. We describe the maximum invariant subspace for a contraction T on which T is a partial isometry to obtain that, in…

In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the…

We study the boundedness of commutators of the Hardy-Littlewood maximal function and the sharp maximal function on weighted Morrey spaces when the symbols of the commutators belong to weighted Lipschitz spaces. Some new characterizations…

Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the operators' symbols. The flexibility and…

We consider a rather general version of ladder operator $Z$ used by some authors in few recent papers, $[H_0,Z]=\lambda Z$ for some $\lambda\in\mathbb{R}$, $H_0=H_0^\dagger$, and we show that several interesting results can be deduced from…

In this paper, we establish a Minkowski-type inequality for weak Lebesgue space, which allows us to obtain a characterization of relative compactness in these spaces. Furthermore, we are the first to investigate the compactness results of…

A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…

We study the space of functions $\phi\colon \NN\to \CC$ such that there is a Hilbert space $H$, a power bounded operator $T$ in $B(H)$ and vectors $\xi,\eta$ in $H$ such that $$\phi(n) = < T^n\xi,\eta>.$$ This implies that the matrix…

We characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on…

We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…

Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum…

We prove an upper bound on the sum of the distances between the eigenvalues of a perturbed Schr\"odinger operator $H_0-V$ and the lowest eigenvalue of $H_0$. Our results hold for operators $H_0=-\Delta-V_0$ in one dimension with single-well…

Covering ill-posed problems with compact and non-compact operators regarding the degree of ill-posedness is a never ending story written by many authors in the inverse problems literature. This paper tries to add a new narrative and some…

We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a…

Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…

A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…