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Anatoly Kochubei
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There exist further generalizations but they do not go very far from AW*-algebras. See

http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.pjm/1102650543 and

http://dmle.cindoc.csic.es/pdf/PUBLICACIONSMATEMATIQUES_1995_39_01_01.pdf

Anatoly Kochubei
  • 4.9k
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  • 23