Isomorphisms of spectral lattices
Operator Algebras
2022-07-11 v2 Functional Analysis
Abstract
The paper deals with spectral order isomorphisms between certain spectral sublattices of direct sums of AW*-factors. We prove that these maps consist of spectral order isomorphisms between spectral sublattices of individual direct summands. Consequently, we obtain a complete description of spectral order isomorphisms in the case of atomic AW*-algebras. This includes the setting of matrix algebras. Moreover, we also exhibit the general form of spectral order orthoisomorphisms between various spectral sublattices of direct sums of AW*-factors.
Keywords
Cite
@article{arxiv.2201.04509,
title = {Isomorphisms of spectral lattices},
author = {Martin Bohata},
journal= {arXiv preprint arXiv:2201.04509},
year = {2022}
}
Comments
Some misprints were corrected and references were updated