Volume 3, Issue 5, September 2018, Page: 102-112
A Note on Some Equivalences of Operators and Topology of Invariant Subspaces
Bernard Mutuku Nzimbi, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Received: Jan. 8, 2018;       Accepted: Feb. 7, 2018;       Published: Dec. 28, 2018
DOI: 10.11648/j.mcs.20180305.12      View  26      Downloads  12
Abstract
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.
Keywords
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
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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