On the fine spectrum of the generalized difference operator over the sequence spaces and .
On the Fine Structure of Spectra.
On the Fredholm alternative for the Fučík spectrum.
On the Gelfand-Hille theorems
On the generalized Drazin inverse and generalized resolvent
We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel....
On the generalized Kato spectrum
2010 Mathematics Subject Classification: 47A10.We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some relationship between this spectrum and the SVEP theory.
On the geometric properties of the joint spectrum of a family of self-adjoint operators
On the growth of the resolvent operators for power bounded operators
Outline. In this paper I discuss some quantitative aspects related to power bounded operators T and to the decay of . For background I refer to two recent surveys J. Zemánek [1994], C. J. K. Batty [1994]. Here I try to complement these two surveys in two different directions. First, if the decay of is as fast as O(1/n) then quite strong conclusions can be made. The situation can be thought of as a discrete version of analytic semigroups; I try to motivate this in Section 1 by demonstrating the...
On the joint spectral radius of commuting matrices
For a commuting n-tuple of matrices we introduce the notion of a joint spectral radius with respect to the p-norm and prove a spectral radius formula.
On the largest analytic set for cyclic operators.
On the largest generalized joint spectrum
On the local spectral properties of weighted shift operators
We study the local spectral properties of both unilateral and bilateral weighted shift operators.
On the method of least squares of finding eigenvalues and eigenfunctions of some symmetric operators. II.
On the multiplication operators on spaces of analytic functions
We consider Hilbert spaces of analytic functions on a plane domain Ω and multiplication operators on such spaces induced by functions from . Recently, K. Zhu has given conditions under which the adjoints of multiplication operators on Hilbert spaces of analytic functions belong to the Cowen-Douglas classes. In this paper, we provide some sufficient conditions which give the converse of the main result obtained by K. Zhu. We also characterize the commutant of certain multiplication operators.
On the norm-closure of the class of hypercyclic operators
Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if is connected, where denotes the Weyl spectrum of T.
On the orbits of an operator with spectral radius one
On the o-Spectrum of Order Bounded Operators.
On the point spectrum of self-adjoint extensions.
On the poles of the local resolvent.
On the power boundedness of certain Volterra operator pencils
Let V be the classical Volterra operator on L²(0,1), and let z be a complex number. We prove that I-zV is power bounded if and only if Re z ≥ 0 and Im z = 0, while I-zV² is power bounded if and only if z = 0. The first result yields as n → ∞, an improvement of [Py]. We also study some other related operator pencils.