Remarks on A-skew-adjoint, A-almost Similarity Equivalence and Other Operators in Hilbert Space
Pure and Applied Mathematics Journal
Volume 6, Issue 3, June 2017, Pages: 101-107
Received: Apr. 28, 2017; Accepted: May 9, 2017; Published: Jun. 29, 2017
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Authors
Isaiah Nalianya Sitati, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Bernard Nzimbi, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Stephen Luketero, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Jairus Khalagai, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
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Abstract
In this paper, notions of A-almost similarity and the Lie algebra of A-skew-adjoint operators in Hilbert space are introduced. In this context, A is a self-adjoint and an invertible operator. It is shown that A-almost similarity is an equivalence relation. Conditions under which A-almost similarity implies similarity are outlined and in which case their spectra is located. Conditions under which an A-skew adjoint operator reduces to a skew adjoint operator are also given. By relaxing some conditions on normal and unitary operators, new results on A -normal, binormal and A-binormal operators are proved. Finally A-skew adjoint operators are characterized and the relationship between A-self- adjoint and A-skew adjoint operators is given.
Keywords
Skew-adjoint, A-skew-adjoint, A-almost Similarity, Hilbert Space, A-Normal and Binormal
To cite this article
Isaiah Nalianya Sitati, Bernard Nzimbi, Stephen Luketero, Jairus Khalagai, Remarks on A-skew-adjoint, A-almost Similarity Equivalence and Other Operators in Hilbert Space, Pure and Applied Mathematics Journal. Vol. 6, No. 3, 2017, pp. 101-107. doi: 10.11648/j.pamj.20170603.12
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Copyright © 2017 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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