Department of Mathematics and Statistics, Colby College, Waterville, ME 04901, USA.
Abstract
The main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. The methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [B. R. Yahaghi, Near triangularizability implies triangularizability, Canad. Math. Bull. 47, (2004), no. 2, 298--313], and [A. A. Jafarian, H. Radjavi, P. Rosenthal and A. R. Sourour, Simultaneous, triangularizability, near commutativity and Rota's theorem, Trans. Amer. Math. Soc. 347, (1995), no. 6, 2191--2199] on the approximations and triangularizability of collections of operators and matrices. In conclusion we introduce and explore a related topology on the power sets of metric spaces.
Livshits, L. (2015). A note on approximation conditions, standard triangularizability and a power set topology. Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), 133-153.
MLA
Livshits, L. "A note on approximation conditions, standard triangularizability and a power set topology", Bulletin of the Iranian Mathematical Society, 41, Issue 7 (Special Issue), 2015, 133-153.
HARVARD
Livshits L. (2015). 'A note on approximation conditions, standard triangularizability and a power set topology', Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), pp. 133-153.
CHICAGO
L. Livshits, "A note on approximation conditions, standard triangularizability and a power set topology," Bulletin of the Iranian Mathematical Society, 41 Issue 7 (Special Issue) (2015): 133-153,
VANCOUVER
Livshits L. A note on approximation conditions, standard triangularizability and a power set topology. BIMS. 2015;41(Issue 7 (Special Issue)):133-153.
