Displaying similar documents to “On spectral properties of linear combinations of idempotents”

Spectral mapping framework

Anar Dosiev (2005)

Banach Center Publications

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In this paper we suggest a general framework of the spectral mapping theorem in terms of parametrized Banach space bicomplexes.

Spectra of the difference, sum and product of idempotents

Mohamed Barraa, Mohamed Boumazgour (2001)

Studia Mathematica

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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.

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.

Perturbation and spectral discontinuity in Banach algebras

Rudi Brits (2011)

Studia Mathematica

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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...

Maps on idempotent operators

Peter Šemrl (2007)

Banach Center Publications

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The set of all bounded linear idempotent operators on a Banach space X is a poset with the partial order defined by P ≤ Q if PQ = QP = P. Another natural relation on the set of idempotent operators is the orthogonality relation defined by P ⊥ Q ⇔ PQ = QP = 0. We briefly survey known theorems on maps on idempotents preserving order or orthogonality. We discuss some related results and open problems. The connections with physics, geometry, theory of automorphisms, and linear preserver...