A quick and simple proof of Sherman's theorem on order in {$C\sp *$}-algebras | Zendy

Wiebe R. Pestman | Zendy

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A quick and simple proof of Sherman's theorem on order in {$C\sp *$}-algebras

Author(s) -

Wiebe R. Pestman

Publication year - 1996

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1105554413

Subject(s) - cone (formal languages) , mathematics , hermitian matrix , simple (philosophy) , vector space , space (punctuation) , order (exchange) , pure mathematics , element (criminal law) , combinatorics , calculus (dental) , algebra over a field , discrete mathematics , computer science , algorithm , philosophy , law , epistemology , political science , operating system , medicine , dentistry , finance , economics

Let AH be the real linear space of all Hermitian elements in A . Now AH = A+−A+; in a natural way AH is an ordered topological vector space with positive cone A+ (see [3], [6], [8]). The cone of all positive linear forms on AH will be denoted by P . Restriction of a positive linear form on A to AH gives an element ∗Work done as a student at the University of Groningen (the Netherlands). Received by the editors September 1995. Communicated by J. Schmets. 1991 Mathematics Subject Classification : 46L05, 46A40.

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