Invertibility in the Algebra of τ-measurable Operators

Abstract

Let \( \mathcal{M} \) be a semi-finite von Neumann algebra in a Hilbert space H and τ be a faithful normal semi-finite trace on \( \mathcal{M} \). The algebra of τ-measurable operators affiliated with \( \mathcal{M} \), equipped with the topology of convergence in measure, is a topological*-algebra. We show that inversion is continuous on Q, the set of invertible elements in , and that Q is open if and only if .Mathematics Subject Classification (2000)Primary 47L60Secondary 46B5Keywordsvon Neumann algebraτ-measurable operatorinvertibility