A-numerical radius inequalities for semi-Hilbertian space operators

In this paper, we aim to introduce the notion of the spectral radius of bounded linear operators acting on a complex Hilbert space $$\mathcal {H}$$
 , which are bounded with respect to the seminorm induced by a positive operator A on $$\mathcal {H}$$
 . Mainly, we show that $$r_A(T)\le \omega _A(T)$$
 for every A-bounded operator T, where $$r_A(T)$$
 and $$\omega _A(T)$$
 denote respectively the A-spectral radius and the A-numerical radius of T. This allows to establish that $$r_A(T)=\omega _A(T)=\Vert T\Vert _A$$
 for every A-normaloid operator T, where $$\Vert T\Vert _A$$
 is denoted to be the A-operator seminorm of T. Moreover, some characterizations of A-normaloid and A-spectraloid operators are given.

Spectral radius of semi-Hilbertian space operators and its applications

In this paper, we introduce the concept of normality of a d-tuple of bounded linear operators acting on a complex Hilbert space H when an additional semi-inner product induced by a positive operato...

Joint normality of operators in semi-Hilbertian spaces

We consider the semiclassical Schrodinger operator with a well in an island potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginary part of the shape resonance at the bottom of the well. This is a generalization of the result by Helffer and Sjostrand [HeSj1] in the globally analytic case. We use an almost-analytic extension in order to continue the WKB solution coming from the well beyond the caustic set, and, for the justification of the accuracy of this approximation, we develop some refined microlocal arguments in h-dependent small regions.

/pdf/width-of-shape-resonances-for-non-globally-analytic-2vo64y8oo8.pdf

Width of shape resonances for non globally analytic potentials

Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces

Joint numerical ranges of operators in semi-Hilbertian spaces

On joint spectral radius of commuting operators in Hilbert spaces

Spectral analysis of bounded operators on semi-Hilbertian spaces

Given a positive operator A on a Hilbert space, we introduce the notion of an A-closed linear operator as a natural extension of the usual notion of an A-bounded operator. We summarize a number of ...

Hamadi Baklouti

Papers

Joint numerical ranges of operators in semi-Hilbertian spaces

Joint normality of operators in semi-Hilbertian spaces

On joint spectral radius of commuting operators in Hilbert spaces

Spectral analysis of bounded operators on semi-Hilbertian spaces

Closed operators in semi-Hilbertian spaces