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ON THE SUBMULTIPLICATIVITY AND SUBADDITIVITY OF THE CONE SPECTRAL RADIUS

By Marko Kandić and Aljosa Peperko

Abstract

Let S be a cone equipped with an associative product ∗ and let p: S → [0, ∞) be a monote ∗-submultiplicative seminorm. We introduce the notion of the cone spectral radius rp associated to p and ∗. We prove that under certain conditions the inequalities rp(a ∗ b) ≤ rp(a)rp(b) and rp(a + b) ≤ rp(a) + rp(b) hold. Our results apply to several radii appearing in the literature including the spectral radius of positive operators, the spectral radius in max algebra, the Bonsall‘s cone spectral radius and the essential cone spectral radius. We also obtain new results in the setting of general Banach algebras

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.417.7487
Provided by: CiteSeerX
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