Simultaneous triangularizability, near commutativity and Rota’s theorem

Jafarian, A. A.; Radjavi, H.; Rosenthal, P.; Sourour, A. R.

doi:10.1090/S0002-9947-1995-1257112-5

Simultaneous triangularizability, near commutativity and Rota’s theorem
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by A. A. Jafarian, H. Radjavi, P. Rosenthal and A. R. Sourour PDF

Trans. Amer. Math. Soc. 347 (1995), 2191-2199 Request permission

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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