Matrix systems, algebras, and open maps
Functional Analysis
2025-06-23 v3 Quantum Physics
Abstract
Every state on the algebra of complex nxn matrices restricts to a state on any matrix system. Whereas the restriction to a matrix system is generally not open, we prove that the restriction to every *-subalgebra of is open. This simplifies topology problems in matrix theory and quantum information theory.
Cite
@article{arxiv.2502.01761,
title = {Matrix systems, algebras, and open maps},
author = {Stephan Weis},
journal= {arXiv preprint arXiv:2502.01761},
year = {2025}
}
Comments
27 pages; version 2: corrections in Section 9 (among others, reference [51] added); version 3: minor corrections in Section 9; comments welcomed