Related papers: Foguel-type operators similar to contractions
The present paper aims to understand separability and entanglement in tensor cones, in the sense of Namioka and Phelps, that arise from the base cones of operator system tensor products. Of particular interest here are the Toeplitz and…
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. \ We first establish a criterion on the coprime-ness of two singular inner functions and…
Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…
In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the…
Contractions (and graded contractions) of Lie algebra, Lie bialgebra and Hopf algebra are discussed. It is noticed the fundamental role of E.In{\"o}n{\"u} and E.P.Wigner idea of degenerate transformations. A constructive algorithm for…
We consider the class of bounded self-adjoint Hankel operators $\mathbf H$, realised as integral operators on the positive semi-axis, that commute with dilations by a fixed factor. By analogy with the spectral theory of periodic…
Generalized Toeplitz plus Hankel operators $T(a)+H_{\alpha}(b)$ generated by functions $a,b$ and a linear fractional Carleman shift $\alpha$ changing the orientation of the unit circle $\mathbb{T}$ are considered on the Hardy spaces…
We consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the class (e.g., closure under taking inverses, resolvents) are…
Using a similarity transformation that maps the Calogero model into $N$ decoupled quantum harmonic oscillators, we construct a set of mutually commuting conserved operators of the model and their simultaneous eigenfunctions. The…
We construct explicit differential operators on hermitian modular forms, extending methods developed for Siegel modular forms. These differential operators are closely related to the two-variable spherical pluriharmonic polynomials. We…
In this article, by considering $T=(T_1,\dots, T_d)$, an $d$-tuple of commuting contractions on a Hilbert space $\mathcal{H}$, we study $T$-Toeplitz operators which consists of bounded operators $X$ on $\mathcal{H}$ such that \[ T_i^*XT_i=X…
$\mathcal{O}$-operators are important in broad areas in mathematics and physics, such as integrable systems, the classical Yang-Baxter equation, pre-Lie algebras and splitting of operads. In this paper, a deformation theory of…
We study composition operators on the Fock spaces $\mathcal{F}^2_\alpha(\mathbb{C}^n)$, problems considered include the essential norm, normality, spectra, cyclicity and membership in the Schatten classes. We give perfect answers for these…
Consider the Fourier transform on the group $GL(2,R)$ of real $2\times 2$-matrices. We show that Fourier-images of polynomial differential operators on $GL(2,R)$ are differential-difference operators with coefficients meromorphic in…
In this paper, we study complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we give a characterization of complex symmetric block Toeplitz operators with the special conjugation on the vector-valued Hardy…
We generalize several results on Toeplitz operators over reflexive, standard weighted Fock spaces $F_t^p$ to the non-reflexive cases $p = 1, \infty$. Among these results are the characterization of compactness and the Fredholm property of…
Our research builds upon Halmos's foundational work on functional monadic Boolean algebras and our previous work on tense operators to develop three essential constructions, including the important concepts of fuzzy sets and powerset…
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…