Selbstadjungierte Operatoren als ?dual" rein atomare Skalaroperatoren.
Selfadjoint Means and Operator Monotone Functions.
Semilinear relations and *-representations of deformations of so(3)
We study a family of commuting selfadjoint operators , which satisfy, together with the operators of the family , semilinear relations , (, , are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra .
Semi-spectral integrals and related mappings
Separate and joint similarity to families of normal operators
Sets of bounded linear operators , ⊂ ℬ(H) (ℋ is a Hilbert space) are similar if there exists an invertible (in ℬ(H)) operator G such that . A bounded operator is scalar if it is similar to a normal operator. is jointly scalar if there exists a set ⊂ ℬ(H) of normal operators such that and are similar. is separately scalar if all its elements are scalar. Some necessary and sufficient conditions for joint scalarity of a separately scalar abelian set of Hilbert space operators are presented (Theorems...
Smooth operators and commutators
Some Berezin number inequalities for operator matrices
Some functions of eigenvalues of normal operator
Kellogg's iterations in the eigenvalue problem are discussed with respect to the boundary spectrum of a linear normal operator.
Some remarks concerning the Large Sieve type
Some remarks on Gleason measures
This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.
Some spectral inequalities involving generalized scalar operators
In 1971, Allan Sinclair proved that for a hermitian element h of a Banach algebra and λ complex we have ∥λ + h∥ = r(λ + h), where r denotes the spectral radius. Using Levin's subordination theory for entire functions of exponential type, we extend this result locally to a much larger class of generalized spectral operators. This fundamental result improves many earlier results due to Gelfand, Hille, Colojoară-Foiaş, Vidav, Dowson, Dowson-Gillespie-Spain, Crabb-Spain, I. & V. Istrăţescu, Barnes,...
Sous-espaces invariants dans les espaces de Banach
Sous-groupes distingues du groupe unitaire et du groupe général linéaire d'un espace de Hilbert quaternionien.
Sous-groupes distingués du groupe unitaire et du groupe général linéaire d'un espace de Hilbert
Sous-normalité jointe non bornée et applications
T. Trent gave a new characterization of subnormality for an operator on a Hilbert space. T. Bînzar and D. Păunescu generalized this condition to commuting triples of operators. Here, we give an n-variable unbounded version of the above results. Theorems of this kind have also been obtained by Z. J. Jabłoński and J. Stochel.
Spectra of observables in the -oscillator and -analogue of the Fourier transform.
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.
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 distribution of the free Jacobi process associated with one projection
Given an orthogonal projection P and a free unitary Brownian motion in a W*-non commutative probability space such that Y and P are *-free in Voiculescu’s sense, we study the spectral distribution νₜ of Jₜ = PYₜPYₜ*P in the compressed space. To this end, we focus on the spectral distribution μₜ of the unitary operator SYₜSYₜ*, S = 2P - 1, whose moments are related to those of Jₜ via a binomial-type expansion already obtained by Demni et al. [Indiana Univ. Math. J. 61 (2012)]. In this connection,...
Spectral integration and spectral theory for non-Archimedean Banach spaces.