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Journal of the London Mathematical Society 1992 s2-46(3):491-498; doi:10.1112/jlms/s2-46.3.491
© 1992 by London Mathematical Society
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© Oxford University Press

Best Approximations in Preduals of Von Neumann Algebras

Alvaro Arias and Vania Mascioni

Department of Mathematics, Texas A&M University College Station, Texas 77843, USA
Department of Mathematics, University of Zurich RamiistraBe 74, CH-9001 Zurich, Switzerland

This paper characterises the semi-Chebychev subspaces of preduals of von Neumann algebras. As an application it generalises the theorem of Doob, that says that Formula has unique best approximations in L1(T), to a large class of preannihilators of natural non-selfadjoint operator algebras including the nest algebras. Then it studies the semi-Chebychev subspaces of the trace class operators and shows that the only Chebychev *-diagrams are ‘triangular".

Department of Mathematics, Statistics and Computing Science, University of Texas at San Antonio, San Antonio TX, USA

Department of Mathematics, University of Texas at Austin, Austin TX, USA


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