Best Approximations in Preduals of Von Neumann Algebras

1992/12/01 by Alvaro Arias, Vania Mascioni
Mathematics · #Advanced Operator Algebra Research #Spectral Theory in Mathematical Physics #Advanced Topics in Algebra

paper · pdf · doi:10.1112/jlms/s2-46.3.491

Abstract

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 H 0 1 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”.

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