Related papers: Hadamard type operators on temperate distributions

We study the spectral properties of positive absolutely minimum attaining operators defined on infinite dimensional complex Hilbert spaces and using that derive a characterization theorem for such type of operators. We construct several…

On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite…

The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…

We consider linear spectral-meromorphic (s-meromorphic) OD operators at the real axis such that all local solutions to the eigenvalue problems are meromorphic for all $\lambda$. By definition, rank one algebro-geometrical operator $L$ admit…

We show that all Hankel operators $H$ realized as integral operators with kernels $h(t+s)$ in $L^2 ({\Bbb R}_{+}) $ can be quasi-diagonalized as $H= {\sf L}^* \Sigma {\sf L} $. Here ${\sf L}$ is the Laplace transform, $\Sigma$ is the…

We consider the Hodge Laplacian $\Delta$ on the Heisenberg group $H_n$, endowed with a left-invariant and U(n)-invariant Riemannian metric. For $0\le k\le 2n+1$, let $\Delta_k$ denote the Hodge Laplacian restricted to $k$-forms. Our first…

Let $\mathcal{M}$ be a semifinite von Neumann algebra on a Hilbert space $\mathcal{H}$ equipped with a faithful normal semifinite trace $\tau$, $S(\mathcal{M},\tau)$ be the ${}^*$-algebra of all $\tau$-measurable operators. Let…

We extend our combinatorial approach of decomposing the partition function of the Potts model on finite two-dimensional lattices of size L x N to the case of toroidal boundary conditions. The elementary quantities in this decomposition are…

We analyze degenerate, second-order, elliptic operators $H$ in divergence form on $L_2({\bf R}^{n}\times{\bf R}^{m})$. We assume the coefficients are real symmetric and $a_1H_\delta\geq H\geq a_2H_\delta$ for some $a_1,a_2>0$ where \[…

An equivalent formulation of the von Neumann inequality states that the backward shift $S^*$ on $\ell_{2}$ is extremal, in the sense that if $T$ is a Hilbert space contraction, then $\|p(T)\| \leq \|p(S^*)\|$ for each polynomial $p$. We…

For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation $RLL=LLR$, the trace of the L-operator gives a…

The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator…

Let T be a quasidiagonal operator on a separable Hilbert space. Then T is the norm limit of operators, each of which generate a finite dimensional C*-algebra, if and only if the C*-algebra generated by T is exact.

The paper deal with the noncommutative Fr\'echet ${}^*$-algebra $\mathcal{L}(s',s)$ of the so-called smooth operators, i.e. linear and continuous operators acting from the space $s'$ of slowly increasing sequences to the Fr\'echet space $s$…

The spectral bound, s(a A + b V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in b \in R. This is shown here, through an elementary lemma, to imply that s(a…

By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs), which take the form $\int dx\, f(x) \mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density…

In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects. Our main result is the construction of an algebra of difference…

Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…

In this paper we define $\lambda$-hyponormal operators on an infinite dimensional Hilbert space $\mathcal{H}$ and find a class of $\lambda$-hyponormal operators that can not be hypercyclic. Also, we study closedness of range and…

Generalized PT-symmetric operators acting an a Hilbert space $\mathfrak{H}$ are defined and investigated. The case of PT-symmetric extensions of a symmetric operator $S$ is investigated in detail. The possible application of the…