Spectral order on AW*-algebras and its preservers
- Authors: Hamhalter J.1,2, Turilova E.1,2
-
Affiliations:
- Department of Mathematics
- Department of Mathematical Statistics
- Issue: Vol 37, No 4 (2016)
- Pages: 439-448
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198059
- DOI: https://doi.org/10.1134/S1995080216040107
- ID: 198059
Cite item
Abstract
We study the spectral order on the set of positive contractions in an AW*-algebra. We introduce the concept of lattice theoretic center of the resulting spectral lattice and show that it coincides with the algebraic center of the underlying AW*-algebra A if A is finite. By applying this result we generalize hitherto known characterizations of preserves of the spectral order by showing that any bijection φ acting on the spectral lattice of a finite AW*-algebra that preserves spectral order and orthogonality in both directions is a composition of function calculus and a Jordan *-isomorphism. We show that this result holds in a wide context of all AW*-algebras provided that φ preserves in addition the multiples of unity.
Keywords
About the authors
J. Hamhalter
Department of Mathematics; Department of Mathematical Statistics
Author for correspondence.
Email: hamhalte@math.feld.cvut.cz
Czech Republic, Technicka 2, 166 27 Prague 6, Prague; Kremlevskaya ul. 35, Kazan, Tatarstan, 420008
E. Turilova
Department of Mathematics; Department of Mathematical Statistics
Email: hamhalte@math.feld.cvut.cz
Czech Republic, Technicka 2, 166 27 Prague 6, Prague; Kremlevskaya ul. 35, Kazan, Tatarstan, 420008