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.
Published in | Pure and Applied Mathematics Journal (Volume 6, Issue 3) |
DOI | 10.11648/j.pamj.20170603.12 |
Page(s) | 101-107 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2017. Published by Science Publishing Group |
Skew-adjoint, A-skew-adjoint, A-almost Similarity, Hilbert Space, A-Normal and Binormal
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APA Style
Isaiah Nalianya Sitati, Bernard Nzimbi, Stephen Luketero, Jairus Khalagai. (2017). Remarks on A-skew-adjoint, A-almost Similarity Equivalence and Other Operators in Hilbert Space. Pure and Applied Mathematics Journal, 6(3), 101-107. https://doi.org/10.11648/j.pamj.20170603.12
ACS Style
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 Appl. Math. J. 2017, 6(3), 101-107. doi: 10.11648/j.pamj.20170603.12
AMA Style
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 Appl Math J. 2017;6(3):101-107. doi: 10.11648/j.pamj.20170603.12
@article{10.11648/j.pamj.20170603.12, author = {Isaiah Nalianya Sitati and Bernard Nzimbi and Stephen Luketero and Jairus Khalagai}, title = {Remarks on A-skew-adjoint, A-almost Similarity Equivalence and Other Operators in Hilbert Space}, journal = {Pure and Applied Mathematics Journal}, volume = {6}, number = {3}, pages = {101-107}, doi = {10.11648/j.pamj.20170603.12}, url = {https://doi.org/10.11648/j.pamj.20170603.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170603.12}, 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.}, year = {2017} }
TY - JOUR T1 - Remarks on A-skew-adjoint, A-almost Similarity Equivalence and Other Operators in Hilbert Space AU - Isaiah Nalianya Sitati AU - Bernard Nzimbi AU - Stephen Luketero AU - Jairus Khalagai Y1 - 2017/06/29 PY - 2017 N1 - https://doi.org/10.11648/j.pamj.20170603.12 DO - 10.11648/j.pamj.20170603.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 101 EP - 107 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20170603.12 AB - 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. VL - 6 IS - 3 ER -