Open Access

# Decomposition of a unitary scalar operator into a product of roots of the identity

### Abstract

We prove that for all $m_1,m_2,m_3 \in \mathbb{N},~ \frac{1}{m_1}+\frac{1}{m_2}+\frac{1}{m_3} \leq 1$, every unitary scalar operator $\gamma I$ on a complex infinite-dimensional Hilbert space is a product $\gamma I = U_1 U_2 U_3$ where $U_i$ is a unitary operator such that $U_i^{m_i} = I$.

Key words: Hilbert space, unitary operator, group representation, string rewriting.

### Article Information

 Title Decomposition of a unitary scalar operator into a product of roots of the identity Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 2, 191-196 MathSciNet MR3098497 zbMATH 1289.47035 Milestones Received 21/01/2013 Copyright The Author(s) 2013 (CC BY-SA)

### Authors Information

D. Yu. Yakymenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

D. Yu. Yakymenko, Decomposition of a unitary scalar operator into a product of roots of the identity, Methods Funct. Anal. Topology 19 (2013), no. 2, 191-196.

### BibTex

@article {MFAT683,
AUTHOR = {Yakymenko, D. Yu.},
TITLE = {Decomposition of a unitary scalar operator into a product of roots of the identity},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {2},
PAGES = {191-196},
ISSN = {1029-3531},
MRNUMBER = {MR3098497},
ZBLNUMBER = {1289.47035},
URL = {http://mfat.imath.kiev.ua/article/?id=683},
}