On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice

Abstract

We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M (with L = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L) * . Our method can be used to prove similar results in finite-dimensional matrix algebras. As a consequence, we give a new proof to the main theorem by Hou and Zhang (2012). KeywordsKadison-Singer algebra, Kadison-Singer lattice, reflexive algebra, double triangle lattice, factor of type II 1 MSC(2010) 47L35, 47L75, 46L10Citation: Dong A J, Wang D. On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice.