Indexed by:Journal Papers
Date of Publication:2020-12-29
Journal:PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume:148
Issue:7
Page Number:2901-2908
ISSN No.:0002-9939
Key Words:Factor von Neumann alegbras; irreducible operators
Abstract:Let M be a factor acting on a complex, separable Hilbert space H. An operator a is an element of M is said to be irreducible in M if W*(a), the von Neumann subalgebra generated by a in M, is an irreducible subfactor of M, i.e., W*(a)' boolean AND M = CI. In this note, we prove that each operator a is an element of M is a sum of two irreducible operators in M, which can be viewed as a natural generalization of a theorem in [Proc. Amer. Math. Soc. 21 (1969), pp. 251-252], with a completely different proof.