Abstract
Suppose that and are positive operators on an ordered Banach space with a normal and generating cone satisfying . It is known that, in this case, we have
In this article we consider less restrictive assumptions on and which give us the same inequalities as above. Moreover, we also prove these inequalities in a more general setting of ordered algebras, and we consider related results in the Banach algebra setting. We apply our results to the essential spectral radius of AM-compact operators and prove the equality under reasonable assumptions.
Citation
Marko Kandić. Aljoša Peperko. "On the submultiplicativity and subadditivity of the spectral and essential spectral radius." Banach J. Math. Anal. 10 (1) 133 - 146, January 2016. https://doi.org/10.1215/17358787-3345005
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