Related papers: Hyponormal contractions and analytic shifts
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
In this paper we characterize those positive operators which are asymptotic limits of contractions in strong operator topology or uniform topology. We examine the problem when the asymptotic limits of two contractions coincide.
In this note, we give an example of a densely defined closed one-to-one paranormal operator $T$ whose adjoint is also injective and paranormal, but $T$ fails to be normal.
Pisier's celebrated counterexample to Halmos's similarity-to-contractions problem was based on $2 \times 2$ upper triangular block operator matrices involving three classical operators: forward and backward shifts on the diagonal and Hankel…
The purpose of the paper is to obtain estimates for differences of functions of two pairs of commuting contractions on Hilbert space. In particular, Lipschitz type estimates, H\"older type estimates, Schatten--von Neumann estimates are…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
We consider weighted shift operators having the property of moment infinite divisibility; that is, for any $p > 0$, the shift is subnormal when every weight (equivalently, every moment) is raised to the $p$-th power. By reconsidering…
Operator $k$-tone functions on an open interval of the real line, which are higher order extensions of operator monotone and convex functions, are characterized via certain inequalities for the real and imaginary parts of analytic…
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…
We give the first example of a quartically hyponormal unilateral weighted shift which is not 3-hyponormal.
The complete characterizations of the spectra and their various parts of hyponormal unilateral and bilateral weighted shifts are presented respectively in this paper. The results obtained here generalize the corresponding work of the…
This paper is devoted to the study of propagation phenomena for $2$--hyponormal, quadratically hyponormal, and cubically hyponormal operator-valued weighted shifts. \ First, we show that every {\it quadratically} hyponormal matrix-valued…
In this paper we consider a problem of the similarity of complex symmetric operators to perturbations of restrictions of normal operators. For a subclass of cyclic complex symmetric operators in a finite-dimensional Hilbert space we prove…
Square of a posinormal operator is not necessarily posinormal$.$ But (i) powers of quasiposinormal operators are quasiposinormal and, under closed ranges assumption, powers of (ii) posinormal operators are posinormal, (iii) of operators…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
In this paper analytic contractions have been established in the $R\to\infty$ contraction limit for exactly solvable basis functions of the Helmholtz equation on the two-dimensional two-sheeted hyperboloid. As a consequence we present some…
In this paper, we study the operator equation $AB=\lambda BA$ for a bounded operator $A,B$ on a complex Hilbert space. We focus on algebraic relations between different operators that include normal, $M$-hyponormal, quasi $*$-paranormal and…
Error estimation of difference operators on irregular nodes is discussed. We can obtain the similar estimates of the errors. However, the error estimate for the difference operators for the second derivatives becomes lower because of…
In this paper, we consider composition operators on weighted Hilbert spaces of analytic functions and observe that a formula for the essential norm, give a Hilbert-Schmidt characterization and characterize the membership in Schatten-class…
Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of…