Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Triangularizable algebras of compact operators


Author: G. J. Murphy
Journal: Proc. Amer. Math. Soc. 84 (1982), 354-356
MSC: Primary 47D30; Secondary 47B05
DOI: https://doi.org/10.1090/S0002-9939-1982-0640229-X
MathSciNet review: 640229
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a closed algebra $ A$ of compact operators is triangularizable if and only if the algebra $ A/\operatorname{rad} (A)$ is commutative.


References [Enhancements On Off] (What's this?)

  • [1] B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math., Springer-Verlag, Berlin and New York, 1979. MR 549769 (81i:46055)
  • [2] M.-D. Choi, C. Laurie and H. Radjavi, On commutators and invariant subspaces, Linear and Multilinear Algebra 9 (1981), 329-340. MR 611266 (82d:47010)
  • [3] H. Dowson, Spectral theory of linear operators, Academic Press, London, 1978. MR 511427 (80c:47022)
  • [4] P. Enflo, On the invariant subspace problem in Banach spaces, Séminaire Maurey-Schwartz (1975-1976), Espaces $ {L^p}$ Applications Radonifiantes et Géométrie des Espaces de Banach, Exp. No. 14-15, Centre Math., École Polytech., Palaiseau, 1976. MR 0473871 (57:13530)
  • [5] P. R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N.J., 1967. MR 0208368 (34:8178)
  • [6] T. J. Laffey, Simultaneous triangularization of matrices-low rank cases and the nonderogatory case, Linear and Multilinear Algebra 6 (1978), 269-305. MR 515915 (80d:15012)
  • [7] C. Laurie, E. Nordgren, H. Radjavi and P. Rosenthal, On triangularization of algebras of operators, preprint. MR 631313 (83d:47014)
  • [8] V. Lomonosov, Invariant subspaces for operators commuting with compact operators, Funkcional. Anal. i Priložen. 7 (1973), 55-56 = Functional Anal. Appl. 7 (1973), 213-214. MR 0420305 (54:8319)
  • [9] N. H. McCoy, On quasi-commutative matrices, Trans. Amer. Math. Soc. 36 (1934), 327-340. MR 1501746
  • [10] -, On the characteristic roots of matrix polynomials, Bull. Amer. Math. Soc. 42 (1963), 592-600.
  • [11] J. R. Ringrose, Super-diagonal forms for compact linear operators, Proc. London Math. Soc. (3) 12 (1962), 367-384. MR 0136998 (25:458)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D30, 47B05

Retrieve articles in all journals with MSC: 47D30, 47B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0640229-X
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society