Matrix systems, algebras, and open maps

• DOI: 10.48550/arxiv.2502.01761
• Publication Date: 2025-01-01
• Authors: Weis, Stephan
• Keywords: Mathematics - Functional Analysis; Quantum Physics; 46A30, 15A60, 47A12, 81P16; FOS: Mathematics; FOS: Physical sciences; Quantum Physics (quant-ph); Functional Analysis (math.FA)

Every state on the algebra $M_n$ 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 $M_n$ is open. This simplifies topology problems in matrix theory and quantum information theory.<br/>26 pages, comments welcomed<br/>