An approximate, multivariable version of Specht's theorem
In this article we provide generalizations of Specht's theorem which states that two n × n matrices A and B are unitarily equivalent if and only if all traces of words in two non-commuting variables applied to the pairs (A, A*) and (B, B*) coincide. First, we obtain conditions which allow us to...
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| Published in | Linear & multilinear algebra Vol. 55; no. 2; pp. 159 - 173 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.03.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0308-1087 1563-5139 |
| DOI | 10.1080/03081080600693285 |
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| Abstract | In this article we provide generalizations of Specht's theorem which states that two n × n matrices A and B are unitarily equivalent if and only if all traces of words in two non-commuting variables applied to the pairs (A, A*) and (B, B*) coincide. First, we obtain conditions which allow us to extend this to simultaneous similarity or unitary equivalence of families of operators, and secondly, we show that it suffices to consider a more restricted family of functions when comparing traces. Our results do not require the traces of words in (A, A*) and (B, B*) to coincide, but only to be close. |
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| AbstractList | In this article we provide generalizations of Specht's theorem which states that two n × n matrices A and B are unitarily equivalent if and only if all traces of words in two non-commuting variables applied to the pairs (A, A*) and (B, B*) coincide. First, we obtain conditions which allow us to extend this to simultaneous similarity or unitary equivalence of families of operators, and secondly, we show that it suffices to consider a more restricted family of functions when comparing traces. Our results do not require the traces of words in (A, A*) and (B, B*) to coincide, but only to be close. |
| Author | Radjavi, H. Marcoux, L. W. Mastnak, M. |
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| Cites_doi | 10.1016/S0022-1236(03)00072-7 10.2140/pjm.1962.12.1405 |
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| Title | An approximate, multivariable version of Specht's theorem |
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