Displaying similar documents to “Spectral mapping framework”

First results on spectrally bounded operators

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

Studia Mathematica

Similarity:

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.

Perturbation and spectral discontinuity in Banach algebras

Rudi Brits (2011)

Studia Mathematica

Similarity:

We extend an example of B. Aupetit, which illustrates spectral discontinuity for operators on an infinite-dimensional separable Hilbert space, to a general spectral discontinuity result in abstract Banach algebras. This can then be used to show that given any Banach algebra, Y, one may adjoin to Y a non-commutative inessential ideal, I, so that in the resulting algebra, A, the following holds: To each x ∈ Y whose spectrum separates the plane there corresponds a perturbation of x, of...

Eventually positive elements in ordered Banach algebras

Gerd Herzog, Peer C. Kunstmann (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In ordered Banach algebras, we introduce eventually and asymptotically positive elements. We give conditions for the following spectral properties: the spectral radius belongs to the spectrum (Perron--Frobenius property); the spectral radius is the only element in the peripheral spectrum; there are positive (approximate) eigenvectors for the spectral radius. Recently such types of results have been shown for operators on Banach lattices. Our results can be viewed as a complement, since...

On the joint spectral radius

Vladimír Müller (1997)

Annales Polonici Mathematici

Similarity:

We prove the p -spectral radius formula for n-tuples of commuting Banach algebra elements

On the characterization of scalar type spectral operators

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

Studia Mathematica

Similarity:

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.