Pure state transformations induced by linear operators

2004/09/01 by Louis E. Labuschagne, Louis Labuschagne, Labuschagne, Louis
Computer Science · Mathematics · Physics and Astronomy · #46L05(Primary) 46L30 #46L52 #47B33(Secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Information and Cryptography #Quantum Mechanics and Applications #math.FA #math.OA #msc:46L30 #msc:46L52

paper · pdf · doi:10.48550/arxiv.math/0409011

24 pages, amslatex, revised and debugged version

openalex publication_date 2004/09/01 · arxiv created 2005/02/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalise Wigner's theorem to its most general form possible for B(h) in the sense of completely characterising those vector state transformations of B(h) that appear as restrictions of duals of linear operators on B(h). We then use this result to similarly characterise the pure state transformations of general C*-algebras that appear as restrictions of duals of linear operators on the underlying algebras. This result may be interpreted as a noncommutative Banach-Stone theorem.

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