# On the Decomposition of Unitary Operators into a Product of Finitely Many Positive Operators

### G. Peltri

Universität Leipzig, Germany

## Abstract

We will show that in an infinite-dimensional separable Hilbert space $\mathcal H$, there exist constants $N \in \mathbb N$ and $c,d \in \mathbb R$ such that every unitary operator can be written as the product of at most $N$ positive invertible operators $\{a_k\} \subseteq B(\mathcal H)$ with $\| a_k \| ≤ c$ and $\|a^{–1}_k \| ≤ d$ for all $k$. 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. 235–248

DOI 10.4171/ZAA/673