Displaying similar documents to “Spectral radius inequalities for positive commutators”

Applications of the spectral radius to some integral equations

Mirosława Zima (1995)

Commentationes Mathematicae Universitatis Carolinae

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In the paper [13] we proved a fixed point theorem for an operator 𝒜 , which satisfies a generalized Lipschitz condition with respect to a linear bounded operator A , that is: m ( 𝒜 x - 𝒜 y ) ≺ A m ( x - y ) . The purpose of this paper is to show that the results obtained in [13], [14] can be extended to a nonlinear operator A .

First results on spectrally bounded operators

M. Mathieu, G. J. Schick (2002)

Studia Mathematica

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A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ Mr(x) for all x ∈ E, where r(·) denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.

On spectral continuity of positive elements

S. Mouton (2006)

Studia Mathematica

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Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least...

On the characterization of scalar type spectral operators

P. A. Cojuhari, A. M. Gomilko (2008)

Studia Mathematica

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The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.