We will show that in an infinite-dimensional separable Hilbert space , there exist constants and such that every unitary operator can be written as the product of at most positive invertible operators with and for all . Some consequences of this result in the context of von Neumann algebras are discussed.
Cite this article
G. Peltri, On the Decomposition of Unitary Operators into a Product of Finitely Many Positive Operators. Z. Anal. Anwend. 14 (1995), no. 2, pp. 235–248DOI 10.4171/ZAA/673