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Spectral isometries

Martin Mathieu (2005)

Banach Center Publications

In this survey, we summarise some of the recent progress on the structure of spectral isometries between C*-algebras.

Spectral localization, power boundedness and invariant subspaces under Ritt's type condition

Yu. Lyubich (1999)

Studia Mathematica

For a bounded linear operator T in a Banach space the Ritt resolvent condition R λ ( T ) C / | λ - 1 | (|λ| > 1) can be extended (changing the constant C) to any sector |arg(λ - 1)| ≤ π - δ, a r c c o s ( C - 1 ) < δ < π / 2 . This implies the power boundedness of the operator T. A key result is that the spectrum σ(T) is contained in a special convex closed domain. A generalized Ritt condition leads to a similar localization result and then to a theorem on invariant subspaces.

Spectral mapping framework

Anar Dosiev (2005)

Banach Center Publications

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

Spectral mapping inclusions for the Phillips functional calculus in Banach spaces and algebras

Eva Fašangová, Pedro J. Miana (2005)

Studia Mathematica

We investigate the weak spectral mapping property (WSMP) μ ̂ ( σ ( A ) ) ¯ = σ ( μ ̂ ( A ) ) , where A is the generator of a ₀-semigroup in a Banach space X, μ is a measure, and μ̂(A) is defined by the Phillips functional calculus. We consider the special case when X is a Banach algebra and the operators e A t , t ≥ 0, are multipliers.

Spectral radius formula for commuting Hilbert space operators

Vladimír Muller, Andrzej Sołtysiak (1992)

Studia Mathematica

A formula is given for the (joint) spectral radius of an n-tuple of mutually commuting Hilbert space operators analogous to that for one operator. This gives a positive answer to a conjecture raised by J. W. Bunce in [1].

Spectral radius inequalities for positive commutators

Mirosława Zima (2014)

Czechoslovak Mathematical Journal

We establish several inequalities for the spectral radius of a positive commutator of positive operators in a Banach space ordered by a normal and generating cone. The main purpose of this paper is to show that in order to prove the quasi-nilpotency of the commutator we do not have to impose any compactness condition on the operators under consideration. In this way we give a partial answer to the open problem posed in the paper by J. Bračič, R. Drnovšek, Y. B. Farforovskaya, E. L. Rabkin, J. Zemánek...

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