Orthogonal Pure States in Operator Theory

2002/11/13 by Jan Hamhalter, Hamhalter, Jan
Mathematics · #46L30 #46L70 #81P10 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L30 #msc:46L70 #msc:81P10

paper · pdf · doi:10.48550/arxiv.math/0211202

9 pages, LATEX

arxiv created 2003/06/05 · arxiv updated 2009/11/30

Abstract

We summarize and deepen recent results on systems of orthogonal pure states on operator algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposining points by continuous functions, separating sets by continuous functions, and multiplicativity of pure states.

Related

• Pure state transformations induced by linear operators
• Restrictions of pure states to subspaces of C^*-algebras
• Nonunital operator systems and noncommutative convexity
• Characterizing locally distinguishable orthogonal product states
• On Characters and Pure States of *-Algebras