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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Simultaneous triangularizability, near commutativity and Rota's theorem


Authors: A. A. Jafarian, H. Radjavi, P. Rosenthal and A. R. Sourour
Journal: Trans. Amer. Math. Soc. 347 (1995), 2191-2199
MSC: Primary 47A66; Secondary 47A45, 47B07, 47B15
MathSciNet review: 1257112
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Abstract: In this paper we consider simultaneously triangularizable collections of compact operators and show that similarities of any finite subcollection can be made arbitrarily close to commuting normal operators. As a consequence, we obtain a variant of a theorem of G.-C. Rota. Also, we give some sufficient conditions for simultaneous triangularization of collections of compact operators. Finally, several counterexamples are given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1257112-5
PII: S 0002-9947(1995)1257112-5
Keywords: Simultaneous triangularizability, near commutativity, compact operators, normal operators
Article copyright: © Copyright 1995 American Mathematical Society