Abstract
Let x and y be elements of an ordered Banach algebra (OBA) such that 0 ≤ x ≤ y. In this paper we will discuss results that give conditions under which the spectral radius of x is a pole of the resolvent of x, given that the spectral radius of y is a pole of the resolvent of y. The results obtained will be used to establish some spectral and asymptotic properties of dominated elements in OBAs.
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© 2016 Springer International Publishing Switzerland
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Muzundu, K. (2016). On Poles of the Resolvents of Dominated Elements in Ordered Banach Algebras. In: de Jeu, M., de Pagter, B., van Gaans, O., Veraar, M. (eds) Ordered Structures and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-27842-1_20
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DOI: https://doi.org/10.1007/978-3-319-27842-1_20
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-27840-7
Online ISBN: 978-3-319-27842-1
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