Related papers: Some classes of weighted conditional type operator…
We obtain some results about the spectrum and the upper semi-Fredholm spectrum of weighted composition operators on uniform algebras, assuming that the corresponding map maps the Shilov boundary onto itself. In particular, it follows from…
We provide a characterisations of nuclear weighted conditional expectation operators between different $L^p(\mu)$-spaces. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted conditional expectation…
By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded…
The weighted numerical radius of a Hilbert space operator has been defined recently. This article explores other properties and uses this newly defined numerical radius to obtain several new interesting inequalities for the weighted…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…
In this paper we study one-point rank one commutative rings of difference operators. We find conditions on spectral data which specify such operators with periodic coefficients.
We show that a compact operator $A$ is a multiple of a positive semi-definite operator if and only if $$ \sigma(AB) \subseteq \overline{W(A)W(B)}, \quad\text{for all (rank one) operators $B$}. $$ An example of a normal operator is given to…
Partial operators can have void or unbounded spectra. Contrarily to what is written in Dunford-Schwarz, the reason is not in the fact they are unounded operators.
We build on a characterization of inner functions $f$ due to Le, in terms of the spectral properties of the operator $V=M_f^*M_f$ and study to what extent the cyclicity on weighted Hardy spaces $H^2_\omega$ of the function $z \mapsto a-z$…
In this paper the spectrum of composition operators on the space of real analytic functions is investigated. In some cases it is completely determined while in some other cases it is only estimated.
In this article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and refine some known results in this field. Among other…
Matrix functions play an increasingly important role in many areas of scientific computing and engineering disciplines. In such real-world applications, algorithms working in floating-point arithmetic are used for computing matrix functions…
We study the spectrum of a periodic non-self-adjoint Dirac operator, and its dependence on a semiclassical parameter is also considered. Several bounds on the spectrum are obtained which provide sharp spectral enclosure estimates.…
In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space…
Bounded composition operators in Paley-Wiener spaces have simple forms, and they are just operators composed through affine mappings of the complex plane. The purpose of this article is to explore some notions about bounded operators and…
A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.
Rank two parametric perturbations of operators and matrices are studied in various settings. In the finite dimensional case the formula for a characteristic polynomial is derived and the large parameter asymptotics of the spectrum is…
In this paper, we first introduce several new classes of weighted amalgam spaces. Then we discuss both strong type and weak type estimates for certain multilinear $\theta$-type Calder\'on--Zygmund operators $T_\theta$ recently introduced in…
We analyze spectral properties of a family of self-adjoint first-order finite difference operators acting on $\ell^2(\mathbb{Z}; \mathbb{C}^2)$ or $\ell^2(\mathbb{Z}_+; \mathbb{C}^2)$. Applying the conjugate operator method, we prove the…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.