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Decomposition of a scalar operator into a product of unitary operators with two points in spectrum |
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| Authors: | Sergio Albeverio Slavik Rabanovich |
| Affiliation: | a Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany b SFB 611, IZKS, Bonn, BiBoS, Bielefeld-Bonn, Germany c CERFIM, Locarno, Accademia di Architettura, USI, Mendrisio, Switzerland d Institute of Mathematics, Ukrainian National Academy of Sciences, 3 Tereshchenkivs’ka, Kyiv 01601, Ukraine |
| Abstract: | We consider products of unitary operators with at most two points in their spectra, 1 and eiα. We prove that the scalar operator eiγI is a product of k such operators if α(1+1/(k-3))?γ?α(k-1-1/(k-3)) for k?5. Also we prove that for eiα≠-1, only a countable number of scalar operators can be decomposed in a product of four operators from the mentioned class. As a corollary we show that every unitary operator on an infinite-dimensional space is a product of finitely many such operators. |
| Keywords: | 15A23 15A24 15A29 47A67 |
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