相关论文: Spectral sets for locally bounded operators

In this paper we develop a version of spectral theory for bounded linear operators on topological vector spaces. We show that the Gelfand formula for spectral radius and Neumann series can still be naturally interpreted for operators on…

If X is a sequentially complete locally convex space, then a quotient bounded operator T is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of the algebra of quotient bounded operators on…

We exhibit a general class of unbounded operators in Banach spaces which can be shown to have the single-valued extension property, and for which the local spectrum at suitable points can be determined. We show that a local spectral radius…

Starting from the classic definitions of local resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and spectrum, the local space and the single-valued extention property of a…

In this paper we give several expressions of spectral radius of a bounded operator on a Hilbert space, in terms of iterates of Aluthge transformation, numerical radius and the asymptotic behavior of the powers of this operator. Also we…

We introduce the spectral points of two-sided positive type of bounded normal operators in Krein spaces. It is shown that a normal operator has a local spectral function on sets which are of two-sided positive type. In addition, we prove…

In this paper, the spectrum, residual spectrum, point spectrum and spectral radius of weighted conditional type operators are computed. As an application, we give an equivalent condition for weighted conditional type operators to be…

We extend the notions of joint and generalized spectral radii to cocycles acting on Banach spaces and obtain a version of Berger-Wang's formula when restricted to the space of cocycles taking values in the space of compact operators.…

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…

Having as start point the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the resolvent set and spectrum of a family of linear bounded operators on a Banach space. In addition,…

General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…

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…

We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known…

Let $\sigma(A)$, $\rho(A)$ and $r(A)$ denote the spectrum, spectral radius and numerical radius of a bounded linear operator $A$ on a Hilbert space $H$, respectively. We show that a linear operator $A$ satisfying $$\rho(AB)\le r(A)r(B)…

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…

We introduce and study the notion of reduced spectral synthesis, which unifies the concepts of spectral synthesis and uniqueness in locally compact groups. We exhibit a number of examples and prove that every non-discrete locally compact…

In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…

Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…

In this paper, we investigate the relation between the Deddens and spectral radius algebras of two bounded linear operators, noting a similarity between them. Additionally, we characterize the Deddens and spectral radius algebras related to…

We completely characterize the Crawford number attainment set and the numerical radius attainment set of a bounded linear operator on a Hilbert space. We study the intersection properties of the corresponding attainment sets of numerical…