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Zeitschrift für Analysis und ihre Anwendungen


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Volume 14, Issue 2, 1995, pp. 235–248
DOI: 10.4171/ZAA/673

Published online: 1995-06-30

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

G. Peltri[1]

(1) Universität Leipzig, Germany

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.

Keywords: Operator theory, von Neumann algebras, non-commutative geometry

Peltri G.: On the Decomposition of Unitary Operators into a Product of Finitely Many Positive Operators. Z. Anal. Anwend. 14 (1995), 235-248. doi: 10.4171/ZAA/673