Further remarks on an order for quantum observables
Operator Algebras
2013-04-03 v2
Abstract
S. Gudder and, later, S. Pulmanova and E. Vincekova, have studied in two recent papers a certain ordering of bounded self-adjoint operators on a Hilbert space. We present some further results on this ordering and show that some structure theorems of the ordered set of operators can be obtained in a more abstract setting of posets having the upper bound property and equipped with a certain orthogonality relation.
Cite
@article{arxiv.1301.0640,
title = {Further remarks on an order for quantum observables},
author = {J. Cirulis},
journal= {arXiv preprint arXiv:1301.0640},
year = {2013}
}
Comments
LaTeX2e; 13 pages, no figures. Submitted to Mathematica Slovaca. Corrected misprints (in particular, in Example 3 on p.12), proof of Theorem 4(b) simplified, an argument improved at the end of Sect.4, Theorem 12 extended, its proof is now more transparent