Some problems of the spectral theory of operator pencils.
Some remarks on the surjectivity spectrum of linear operators
Some results on dominant operators.
Some spectral inclusions on D-commuting systems.
Spectra and Numerical Ranges in Locally M-Convex Algebras
Spectra of operator equations and automorphism groups of von Neumann algebras.
Spectra of partial integral operators with a kernel of three variables
Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in (Ω): (T 1 f)(x, y) = k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = k 2(x, ts, y)f(t, y)dt where k 1 and k 2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT 1, τ ∈ ℂ and E−τT 2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra of bounded...
Spectra of the difference, sum and product of idempotents
We give a simple proof of the relation between the spectra of the difference and product of any two idempotents in a Banach algebra. We also give the relation between the spectra of their sum and product.
Spectra originating from semi-B-Fredholm theory and commuting perturbations
Burgos, Kaidi, Mbekhta and Oudghiri [J. Operator Theory 56 (2006)] provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator F is of power finite rank if and only if for every operator T commuting with F. Later, several authors extended this result to the essential descent spectrum, left Drazin spectrum and left essential Drazin spectrum. In this paper, using the theory of operators with eventual topological uniform descent and the technique used by Burgos et...
Spectral analysis and synthesis
Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems.
Spectral analysis of an operator associated with linear functional differential equations and its applications.
Spectral analysis of unbounded Jacobi operators with oscillating entries
We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the OP family...
Spectral and homological properties of Hilbert modules over the disc algebra
We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective Hilbert modules. Part of our work also addresses the classical derivation problem.
Spectral approximation of positive operators by iteration subspace method
The iteration subspace method for approximating a few points of the spectrum of a positive linear bounded operator is studied. The behaviour of eigenvalues and eigenvectors of the operators arising by this method and their dependence on the initial subspace are described. An application of the Schmidt orthogonalization process for approximate computation of eigenelements of operators is also considered.
Spectral characterization of operators with precompact orbit
Spectral inclusions and stability results for strongly continuous semigroups.
Spectral integration and spectral theory for non-Archimedean Banach spaces.
Spectral invariance for pseudodifferential operators on weighted function spaces.
Spectral isometries
In this survey, we summarise some of the recent progress on the structure of spectral isometries between C*-algebras.