JournalszaaVol. 14, No. 2pp. 235–248

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

  • G. Peltri

    Universität Leipzig, Germany
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Abstract

We will show that in an infinite-dimensional separable Hilbert space H\mathcal H, there exist constants NNN \in \mathbb N and c,dRc,d \in \mathbb R such that every unitary operator can be written as the product of at most NN positive invertible operators {ak}B(H)\{a_k\} \subseteq B(\mathcal H) with akc\| a_k \| ≤ c and ak1d\|a^{–1}_k \| ≤ d for all kk. 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