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Positivity

, Volume 22, Issue 5, pp 1355–1357 | Cite as

A note on Huijsmans-de Pagter problem in ordered Banach algebras

  • Roman Drnovšek
Article

Abstract

We give an example of a positive element a in some ordered Banach algebra \(\mathcal A\) such that its spectrum is equal to \(\{1\}\) and it is not greater than or equal to the unit element of \(\mathcal A\).

Keywords

Ordered Banach algebra Spectrum Positive element 

Mathematics Subject Classification

47B60 47A10 46H05 

Notes

Acknowledgements

The author acknowledges the financial support from the Slovenian Research Agency (Research Core Funding No. P1-0222).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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