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Positivity

, Volume 22, Issue 2, pp 533–549 | Cite as

A note on the lower Weyl and Lozanovsky spectra of a positive element

  • Ronalda Benjamin
  • Sonja Mouton
Article

Abstract

One of the central problems investigated in Alekhno (Positivity 11(3):375–386, 2007, Positivity 13(1):3–20, 2009) is that of providing conditions under which the spectral radius of a positive operator T on a complex Banach lattice lies outside the lower Weyl spectrum of T given that it is not an element of its essential spectrum. In this paper the lower Weyl spectrum of an arbitrary positive ordered Banach algebra element is introduced and studied, and work done in the aforementioned papers are extended to general ordered Banach algebras.

Keywords

Ordered Banach algebra Positive element Fredholm spectrum Lower Weyl spectrum Lozanovsky spectrum 

Mathematics Subject Classification

46H05 47A10 47B65 

Notes

Acknowledgements

The work was supported by the National Research Foundation (NRF) of South Africa (Grant Nos. 84602 and 96130).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesStellenbosch UniversityMatielandSouth Africa

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