A Note on Some Equivalences of Operators and Topology of Invariant Subspaces
Mathematics and Computer Science
Volume 3, Issue 5, September 2018, Pages: 102-112
Received: Jan. 8, 2018; Accepted: Feb. 7, 2018; Published: Dec. 28, 2018
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Bernard Mutuku Nzimbi, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
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In this paper we investigate the invariant and hyperinvariant subspace lattices of some operators. We give a lattice-theoretic description of the lattice of hyperinvariant subspaces of an operator in terms of its lattice of invariant subspaces. We also study the structure of these lattices for operators in certain equivalence classes of some equivalence relations.
Invariant Subspace, Reducing Subspace, Hyperinvariant, Hyper-Reducing, Commutant, Bicommutant, Reducible, Irreducible Operator
To cite this article
Bernard Mutuku Nzimbi, A Note on Some Equivalences of Operators and Topology of Invariant Subspaces, Mathematics and Computer Science. Vol. 3, No. 5, 2018, pp. 102-112. doi: 10.11648/j.mcs.20180305.12
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
H. Bercovici, C. Foias, and C. Pearcy, On the hyperinvariant subspace problem IV, Canadian J. Math. 60 (2008), 758-789.
C. Foias, S. Hamid, C. Onica, and C. Pearcy, Hyperinvaraint subspaces III, J. Functional Anal. 222, No.1 (2005), 129-142.
M. F. Gamal, contractions: A Jordan model and lattices of invariant subspaces, St. Petersburg Math Journal 15 (2004), 773-793.
L. V. Harkrishan, Elements of Hilbert spaces and operators, Springer, Singapore, 2017.
D. Herrero, Quasisimilarity does not preserve the hyperlattice, Proc. Amer. Math. Soc. 65, No.1 (1977), 80-84.
T. B. Hoover, Operator algebras with reducing invariant subspaces, Paci_c J. of Math. 44 (1973), 173-179.
L. Kerchy, On the hyperinvariant subspace problem for asymptotically nonvanishing contractions, Operator Theory: Advances and Applications 127 (2001), 399-422.
C. S. Kubrusly, An introduction to models and decompositions in operator theory, Birkhauser, Boston, 1997.
C. S. Kubrusly, Elements of operator theory, Birkhauser, Basel, Boston, 2001.
C. S. Kubrusly, Hilbert space operators:A problem solving approach, Birkhauser, Basel, Boston, 2003.
C. S. Kubrusly, On similarity to normal operators, Mediterranean J. of Math. (2016), 2073-2085.
W. E. Longstaff, A lattice-theoretic description of the lattice of hyperinvariant subspaces of a linear transformation, Can. J. Math. XXVIII, No. 5 (1976), 1062-1066.
Valentine Matache, Operator equations and invariant subspaces, Le Matematiche XLIX-Fasc. I (1994), 143-147.
A. Mello and C. S. Kubrusly, Quasiaffinity and invariant subspaces, Archiv der Mathematik 107 (2016), 173-184.
R. Moore, Hyperinvariant subspaces of reductive operators, Proc. American Mathematical Society 63, No. 1 (1977), 91-94.
R. Moore, Reductive operators that commute with a compact operator, Michigan Math. J. 22 (1975), 229-233.
M. Sababheh, A. Yousef and R. Khalil, On the invariant subspace problem, Bulletin of the Malaysian Math. Sci. Soc, April 2016, Vol. 39, Issue 2, 699-705.
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