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Semilinear relations and *-representations of deformations of so(3)

Yuriĭ Samoĭlenko, Lyudmila Turowska (1997)

Banach Center Publications

We study a family of commuting selfadjoint operators = ( A k ) k = 1 n , which satisfy, together with the operators of the family = ( B j ) j = 1 n , semilinear relations ⅀ i f i j ( ) B j g i j ( ) = h ( ) , ( f i j , g i j , h j : ℝ n → ℂ 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 U q ' ( s o ( 3 ) ) .

Separate and joint similarity to families of normal operators

Piotr Niemiec (2002)

Studia Mathematica

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 G - 1 · · G = . 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...

Some remarks on Gleason measures

P. De Nápoli, M. C. Mariani (2007)

Studia Mathematica

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

B. Aupetit, D. Drissi (1994)

Studia Mathematica

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-normalité jointe non bornée et applications

Olivier Demanze (2005)

Studia Mathematica

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 the difference, sum and product of idempotents

Mohamed Barraa, Mohamed Boumazgour (2001)

Studia Mathematica

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

Andrzej Pokrzywa (1984)

Aplikace matematiky

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 A n 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 A n is also considered.

Spectral distribution of the free Jacobi process associated with one projection

Nizar Demni, Taoufik Hmidi (2014)

Colloquium Mathematicae

Given an orthogonal projection P and a free unitary Brownian motion Y = ( Y ₜ ) t ≥ 0 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,...

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