On Cardinal Invariants and Generators for von Neumann Algebras

David Sherman
2011 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
We demonstrate how most common cardinal invariants associated to a von Neumann algebra M can be computed from the decomposability number, dec(M), and the minimal cardinality of a generating set, gen(M). Applications include the equivalence of the well-known generator problem, "Is every separably-acting von Neumann algebra singly-generated?", with the formally stronger questions, "Is every countably-generated von Neumann algebra singly-generated?" and "Is the gen invariant monotone?" Modulo the
more » ... otone?" Modulo the generator problem, we determine the range of the invariant (gen(M), dec(M)), which is mostly governed by the inequality dec(M) ≤ c gen(M) . 2000 Mathematics Subject Classification. 46L10.
doi:10.4153/cjm-2011-048-2 fatcat:gpehuqbt4nd3tgqfttt6yknnuq