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On Rank One Commutators and Triangular Representations

Published online by Cambridge University Press:  20 November 2018

Tsoy-Wo Ma
Tsoy-Wo Ma*
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, W.A. 6009, Australia
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Abstract

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Starting with the extension of Lomonosov's Lemma by Tychonoff fixed point theorem, a result of Daughtry and Kim — Pearcy-Shields on rank-one commutators is extended to the context of locally convex spaces. Non-zero diagonal coefficients, eigenvalues and simultaneous triangular representations of compact operators on locally convex spaces are studied.

Keywords

47A1047A67Lomonosov techniquerank one commutatorsinvariant subspacescompact non-selfadjointdiagonal coefficientseigenvaluestriangular representationsRiesz theory
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 3 , 01 September 1986 , pp. 268 - 273
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Brodskii, M. S., Triangular and Jordan Representations of Linear Operators, Amer. Math. Soc. Transi., 32(1971).Google Scholar
2. Daughtry, J., An Invariant Subspace Theorem, Proc. Amer. Math. Soc. 49 (1975), pp. 267 — 268.Google Scholar
3. Fan, K., Invariant Subspaces of Certain Linear Operators, Bull. Amer. Math. Soc. 69 (1963), pp. 69–1963.Google Scholar
4. Gohberg, I.C. and Krein, M. G., Theory and Applications of Vol terra Operators in Hilbert Space, Amer. Math. Soc. Transi., 24 (1970).Google Scholar
5. Kim, H. W., Pearcy, C. and Shields, A. L., Rank One Commutators and Hyperinvariant Subspaces, Mich. Math. J. 22 (1975), pp. 193–194.Google Scholar
6. Köthe, G., Topological Vector Space II, Springer, 1979.Google Scholar
7. Laurie, C., Nordgren, E., Radjavi, H. and Rosenthal, P., On Triangularization of Algebras of Operators, J. Reine Agnew. Math. 327 (1981), pp. 143–155.Google Scholar
8. Lomonosov, V. I., Invariant Subspaces for the Family of Operators Commuting with a Completely Continuous Operator, Funct. Anal, and Appl. 7 (1973), pp. 213–214.Google Scholar
9. McCoy, N. H., On Quasi-Commutative Matrices, Trans. Amer. Math. Soc. 36 (1934), pp. 327–340.Google Scholar
10. McCoy, N. H., On Characteristic Roots of Matrix Polynomials, Bull. Amer. Math. Soc, 42 (1936), pp. 592–600.Google Scholar
11. Ringrose, J. R., Compact Non-Self-Adjoint Operators, Von Nostrand, 1971.Google Scholar
12. Radjavi, H. and Rosenthal, P., Invariant Subspaces, Springer, 1973.Google Scholar
13. Robertson, A. P. and Robertson, W., Topological Vector Spaces, Cambridge, 1973.Google Scholar
14. Schaefer, H. H., Topological Vector Spaces, Macmillan, 1966.Google Scholar
15. Tychonoff, A., Ein Fixpunktsatz, Math. Ann. III (1935), pp. 767–776.Google Scholar