A note on lattice ordered C∗‐algebras and Perron–Frobenius theory

Jochen Glück

Mathematische Nachrichten, 2018, vol. 291, issue 11-12, 1727-1732

Abstract: A classical result of Sherman says that if the space of self‐adjoint elements in a C∗‐algebra A is a lattice with respect to its canonical order, then A is commutative. We give a new proof of this theorem which shows that it is intrinsically connected with the spectral theory of positive operator semigroups. Our methods also show that some important Perron–Frobenius like spectral results fail to hold in any non‐commutative C∗‐algebra.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201700404

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:291:y:2018:i:11-12:p:1727-1732

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().