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The Operator Hilbert Space OH and Type III Von Neumann Algebras
Author(s) -
Pisier Gilles
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930400311x
Subject(s) - mathematics , von neumann's theorem , von neumann algebra , hilbert space , affiliated operator , embedding , operator space , von neumann architecture , abelian von neumann algebra , pure mathematics , operator (biology) , unitary operator , type (biology) , algebra over a field , space (punctuation) , operator algebra , multiplication operator , jordan algebra , finite rank operator , banach space , algebra representation , linguistics , repressor , artificial intelligence , chemistry , computer science , biochemistry , transcription factor , gene , philosophy , ecology , biology
A proof is given to show that the operator Hilbert space OH does not embed completely isomorphically into the predual of a semi‐finite von Neumann algebra. This complements Junge's recent result, which admits such an embedding in the non‐semi‐finite case. 2000 Mathematics Subject Classification 46L07, 46L54, 47L25, 47L50.