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Eventually positive elements in ordered Banach algebras

Gerd Herzog, Peer C. Kunstmann (2023)

Commentationes Mathematicae Universitatis Carolinae

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 our structural...

Exponential bounds for noncommuting systems of matrices

Brian Jefferies (2001)

Studia Mathematica

It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form | | e i T , ζ | | C ( 1 + | ζ | ) s e r | ζ | . The proof appeals to the monogenic functional calculus.

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