On cardinal invariants and generators for von Neumann algebras
Operator Algebras
2019-08-15 v2 Functional Analysis
Abstract
We demonstrate how virtually all 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 generator problem, we determine the range of the invariant (gen(M), dec(M)), which is mostly governed by the inequality dec(M) leq c^{gen(M)}.
Keywords
Cite
@article{arxiv.0908.4565,
title = {On cardinal invariants and generators for von Neumann algebras},
author = {David Sherman},
journal= {arXiv preprint arXiv:0908.4565},
year = {2019}
}
Comments
22 pages; the main additions are Theorem 3.8 and Section 8