On the peripheral spectrum of positive elements

2017/05/17 by Alekhno, Egor A.
#46B40 #46H10 #46H30 #47A10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1705.06602

Abstract

We investigate the peripheral spectrum of irreducible positive elements of an ordered Banach algebra. In particular, we give conditions under which the peripheral spectrum contains (or coincides with) the cyclic group generated by a root of unity, and conditions under which the whole spectrum is invariant under the action of this cyclic group.

Related

• Growth rates and the peripheral spectrum of positive operators
• A note on Huijsmans-de Pagter problem in ordered Banach algebras
• Irreducible Semigroups of Positive Operators on Banach Lattices
• On the spectrum of positive finite-rank operators with a partition of unity property
• A note on the spectrum of irreducible operators and semigroups