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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 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,...

Spectral transition parameters for a class of Jacobi matrices

Joanne Dombrowski, Steen Pedersen (2002)

Studia Mathematica

This paper initially considers a class of unbounded Jacobi matrices defined by an increasing sequence of repeated weights. Spectral parameters are then introduced in various ways to allow the authors to study the nature and location of the spectrum as a function of these parameters.

Stable invariant subspaces for operators on Hilbert space

John B. Conway, Don Hadwin (1997)

Annales Polonici Mathematici

If T is a bounded operator on a separable complex Hilbert space ℋ, an invariant subspace ℳ for T is stable provided that whenever T n is a sequence of operators such that T n - T 0 , there is a sequence of subspaces n , with n in L a t T n for all n, such that P n P in the strong operator topology. If the projections converge in norm, ℳ is called a norm stable invariant subspace. This paper characterizes the stable invariant subspaces of the unilateral shift of finite multiplicity and normal operators. It also shows that...

Subnormal operators, cyclic vectors and reductivity

Béla Nagy (2013)

Studia Mathematica

Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.

Subnormality and cyclicity

Franciszek Hugon Szafraniec (2005)

Banach Center Publications

For an unbounded operator S the question whether its subnormality can be built up from that of every S f , the restriction of S to a cyclic space generated by f in the domain of S, is analyzed. Though the question at large has been left open some partial results are presented and a possible way to prove it is suggested as well.

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