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.
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