Abstract Hermitian Algebras I. Spectral Resolution
| dc.creator | Foulis, David J. | |
| dc.creator | Pulmannova, Sylvia | |
| dc.date | 2007-10-26 | |
| dc.date.accessioned | 2026-07-07T08:38:50Z | |
| dc.date.available | 2026-07-07T08:38:50Z | |
| dc.description | We refer to the real Jordan Banach algebra of bounded Hermitian operators on a Hilbert space as a Hermitian algebra. We define an abstract Hermitian algebra (AH-algebra) to be the directed group of an e-ring that contains a semitransparent element, has the quadratic annihilation property, and satisfies a Vigier condition on pairwise commuting ascending sequences. All of this terminology is explicated in this article, where we launch a study of AH-algebras. Here we establish the fundamental properties of AH-algebras, including the existence of polar decompositions and spectral resolutions, and we show that two elements of an AH-algebra commute if and only if their spectral projections commute. We employ spectral resolutions to assess the structure of maximal pairwise commuting subsets of an AH-algebra. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0710.5062 | |
| dc.identifier | http://arxiv.org/abs/0710.5062 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140874 | |
| dc.subject | Functional Analysis | |
| dc.subject | 06F25; 47B15 | |
| dc.title | Abstract Hermitian Algebras I. Spectral Resolution | |
| dc.type | text |