Related papers: Foguel-type operators similar to contractions

We show that for a given pure contraction $T_7$ acting on a Hilbert space $\mathcal{H}$, if $(\tilde{F}_1, \dots, \tilde{F}_6) \in \mathcal{B}(\mathcal{D}_{T^*_7})$ with $[\tilde{F}_i, \tilde{F}_j] = 0, [\tilde{F}^*_i, \tilde{F}_{7-j}] =…

We consider bisingular pseudodifferential operators which are pseudodifferential operators of tensor product type. These operators are defined on the product manifold $M_1 \times M_2$, for closed manifolds $M_1$ and $M_2$. We prove a…

A $7$-tuple of commuting bounded operators $\mathbf{T} = (T_1, \dots, T_7)$ defined on a Hilbert space $\mathcal{H}$ is said to be a \textit{$\Gamma_{E(3; 3; 1, 1, 1)}$-contraction} if $\Gamma_{E(3; 3; 1, 1, 1)}$ is a spectral set for…

We make a progress towards describing the semi-commutants of Toeplitz operators on Fock-Sobolev spaces of nonnegative orders. We generalize the results in \cite{Bauer1,Qin}. For the certain symbol spaces, we obtain two Toeplitz operators…

In this work, we develop a unified framework for quasidiagonal and F\o lner-type approximations of linear operators on Hilbert spaces. These approximations (originally formulated for bounded operators and operator algebras) involve…

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…

In this paper we obtain a representation as martingale transform operators for the rearrangement and shift operators introduced by T. Figiel. The martingale transforms and the underlying sigma algebras are obtained explicitly by…

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of complex quadratic forms, from the point of view of Fourier integral operators in the complex domain. Sufficient conditions are established for…

This paper presents a comprehensive study of H-Toeplitz operators on the Fock space, a class of operators that synthesizes structural elements of both Toeplitz and Hankel operators. We derive explicit matrix representations for these…

We present a method for the explicit diagonalization of some Hankel operators. This method allows us to recover classical results on the diagonalization of Hankel operators with the absolutely continuous spectrum. It leads also to new…

We introduce an extended class of cross-Toeplitz operators which act between Fock--Segal--Bargmann spaces with different weights. It is natural to consider these operators in the framework of representation theory of the Heisenberg group.…

We investigate the commutativity and semi-commutativity of generalized singular integral operators of the form $P_{+} f P_{+} + P_{-} g P_{+} + P_{+} u P_{-} + P_{-} v P_{-}$ on $L^{2}$, where $P_{+}$ denotes the Riesz projection and…

Functions like the exponential, Chebyshev polynomials, and monomial symmetric polynomials are preeminent among all special functions. They have simple definitions and can be expressed using easily specified integers like n!. Families of…

This paper is about the operators defined between K\"othe spaces whose associated matrix is a Hankel matrix. After demonstrating how these operators are defined, the conditions for continuity and compactness of these operators are…

we show that the definitions of some classes of semi-Fredholm operators, which use the language of algebra and first introduced by X. Fang in [8], are equivalent to that of some well-known operator classes. For example, the concept of…

A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of…

We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with $4 \times 4$ matrix symbols. We discuss their norm, their kernel, Fredhomlness,…

We study the boundedness of Toeplitz-type operators defined in the context of the Calder\'on reproducing formula considering the specific wavelets whose Fourier transforms are related to Laguerre polynomials. Some sufficient conditions for…

In this paper, we obtain the ladder operators and associated compatibility conditions for the type I and the type II multiple orthogonal polynomials. These ladder equations extend known results for orthogonal polynomials and can be used to…

This paper deals with well-known higher-order generalizations of Hankel operators. We show that higher-order Hankel operators can be written explicitly as linear differential operators, and give the exact form of these differential…