相关论文: Integer operators in finite von Neumann algebras
Recent results of L. Zsido, based on his previous work with C. P. Niculescu and A. Stroh, on actions of topological semigroups on von Neumann algebras, give a Jacobs-de Leeuw-Glicksberg splitting theorem at the von Neumann algebra (rather…
Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and…
We reflect real spectra of new logarithmic model PT-symmetry operators with singular and non-singular in nature. We also notice that iso-spectral nature between inverted and non-inverted logarithmic PT-symmetric potentials. Present…
We examine the common null spaces of families of Herz-Schur multipliers and apply our results to study jointly harmonic operators and their relation with jointly harmonic functionals. We show how an annihilation formula obtained in J.…
We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on the Lorentz spaces follows from…
One may obtain, using operator transformations, algebraic relations between the Fourier transforms of the causal propagators of different exactly solvable potentials. These relations are derived for the shape invariant potentials. Also,…
We examine the question of when, and how, the norm of a vector functional on an operator algebra can be controlled by the invariant subspace lattice of the algebra. We introduce a related operator algebraic property, and show that it is…
Many "real" inverse spectral data for periodic finite-gap operators (consisting of Riemann Surface with marked "infinite point", local parameter and divisors of poles) lead to operators with real but singular coefficients. These operators…
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…
We provide a representation of the $C^*$-algebra generated by multidimensional integral operators with piecewise constant kernels and discrete ergodic operators. This representation allows us to find the spectrum and to construct the…
The integration operators (*) $({\mathcal J}^+\,g)(x) = \int_a^x g(t) \, dt$ and (**) $({\mathcal J}^-\,g)(x) = \int_x^b g(t) \, dt$ defined on an interval $(a,b) \subseteq {\mathbf R}$ yield new identities for indefinite convolutions,…
Some special Hilbert spaces are introduced to present the class of infinitesimal operators with complete minimal non-basis family of eigenvectors. The discrete Hardy inequality plays an important role in the proposed approach. The…
We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection…
In this paper we discuss the spectral properties of one-term symmetric differential operators of even order with interior singularity, namely, we determine the deficiency numbers, describe its self-adjoint extensions and their spectrum. It…
We provide criteria for self-adjointness and {\tau}-Fredhomness of first and second order differential operators acting on sections of infinite dimensional bundles, whose fibers are modules of finite type over a von Neumann algebra A…
We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schr\"odinger operators on $[a,\infty)$, $a\in\mathbb{R}$, with a regular finite end point $a$ and the case of Schr\"odinger…
Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…
We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model…
We show that formal Schr\"odinger operators with singular potentials from the space W^{-1}_{2,unif}(R) can be naturally defined to give selfadjoint and bounded below operators, which depend continuously in the uniform resolvent sense on the…
We determine the spectrum of the Voltterra-type integral operators $V_g$ on the growth type Fock--Sobolev spaces $\mathcal{F}_{\psi_m}^\infty$. We also characterized the bounded and compact spectral properties of the operators in terms of…