English

Matrix systems, algebras, and open maps

Functional Analysis 2025-06-23 v3 Quantum Physics

Abstract

Every state on the algebra MnM_n 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 MnM_n is open. This simplifies topology problems in matrix theory and quantum information theory.

Keywords

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

R2 v1 2026-06-28T21:31:14.685Z