Spectral order isomorphisms and AW*-factors
Operator Algebras
2022-07-11 v1
Abstract
The paper deals with spectral order isomorphisms in the framework of AW*-algebras. We establish that every spectral order isomorphism between sets of all self-adjoint operators (or between sets of all effects, or between sets of all positive operators) in AW*-factors of Type I has a canonical form induced by a continuous function calculus and an isomorphism between projection lattices. In particular, this solves an open question about spectral order automorphisms of the set of all (bounded) self-adjoint operators on an infinite-dimensional Hilbert space. We also discuss spectral order isomorphisms preserving, in addition, orthogonality in both directions.
Cite
@article{arxiv.1911.07491,
title = {Spectral order isomorphisms and AW*-factors},
author = {Martin Bohata},
journal= {arXiv preprint arXiv:1911.07491},
year = {2022}
}