Geodesic
A Trace Condition Equivalent to Simultaneous Triangularizability
Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 376-386

Voir la notice de l'article provenant de la source Cambridge University Press

A collection of matrices over a field F is said to be triangularizable if there is an invertible matrix T over F such that the matrices T−1ST, are all upper triangular. It is a well-known and easy fact that any commutative set is triangularizable if F is algebraically closed, or if F contains the spectrum of every member of . Many sufficient conditions are known for triangularizability of matrix collections. Levitzki [7] proved that a (multiplicative) semigroup of nilpotent matrices is triangularizable. (His result is valid even over a division ring.) Kolchin [5] showed the triangularizability of a semigroup of unipotent matrices, i.e., matrices of the form I + N with N nilpotent. Kaplansky [3, 4] unified and generalized these results. 
Radjavi, Heydar. A Trace Condition Equivalent to Simultaneous Triangularizability. Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 376-386. doi: 10.4153/CJM-1986-018-1
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[1] 1. Dunford, N. and Schwartz, J. T., Linear operators, Part II: Spectral theory (Interscience, New York, 1963). Google Scholar

[2] 2. Jacobson, N., Lectures in abstract algebra II: linear algebra (van Nostrand, Princeton, 1953). Google Scholar | DOI

[3] 3. Kaplansky, I., Fields and rings, 2nd Ed. (University of Chicago Press, Chicago, 1972). Google Scholar

[4] 4. Kaplansky, I., The Engel-Kolchin theorem revisited, in Contributions to algebra (Academic Press, New York, 1977). Google Scholar

[5] 5. Kolchin, E., On certain concepts in the theory of algebraic matric groups, Ann. of Math. 49 (1948), 774–789. Google Scholar

[6] 6. Laurie, C., Nordgren, E., Radjavi, H. and Rosenthal, P., On triangularization of algebras of operators, J. Reine Angew. Math. 327 (1981), 143–155. Google Scholar

[7] 7. Levitzki, J., Uber nilpotente Unterringe, Math. Ann. 105 (1931), 620–627. Google Scholar

[8] 8. Lomonosov, V. J., Invariant subspaces for operators commuting with compact operators, Funkcional Anal, i Prilozen 7 (1973), (Russian); Functional Anal. Appl. 7 (1973), 213–214. Google Scholar

[9] 9. McCoy, N. H., On the characteristic roots of matric polynomials, Bull. Amer. Math. Soc. 42 (1936), 592–600. Google Scholar

[10] 10. Nordgren, E., Radjavi, H. and Rosenthal, P., Triangularizing semigroups of compact operators, Indiana Univ. Math. J. 33 (1984), 271–275. Google Scholar

[11] 11. Radjavi, H., Isomorphisms of transitive operator algebras, Duke Math. J. 41 (1974), 555–564. Google Scholar

[12] 12. Radjavi, H., On the reduction and triangularization of semigroups of operators, J. Operator Theory 13 (1985), 63–71. Google Scholar

[13] 13. Radjavi, H. and Rosenthal, P., On transitive and reductive operator algebras, Math. Ann. 209 (1974), 43–56. Google Scholar

[14] 14. Radjavi, H. and Rosenthal, P., Invariant subspaces (Springer-Verlag, New York, 1973). Google Scholar | DOI

[16] 16. Ringrose, J. R., Compact non-self adjoint operators (Van Nostrand, Princeton, 1971). Google Scholar

[17] 17. Watters, J. F., Block triangularization of algebras of matrices, Linear Alg. App. 32 (1980), 3–7 Google Scholar

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