In this paper, we investigate properties of A-self-adjoint operators and other relations on Hilbert spaces. In this context, A is a self-adjoint and an invertible operator. More results on operator equivalences including similarity, unitary and metric equivalences are discussed. We also investigate conditions under which these classes of operators are self- adjoint and unitary. We finally locate their spectra.
| Published in | Mathematics and Computer Science (Volume 1, Issue 3) |
| DOI | 10.11648/j.mcs.20160103.14 |
| Page(s) | 56-60 |
| Creative Commons |
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. |
| Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
A-Self-Adjoint, A-Unitary, Hilbert Space, Metric Equivalence, Quasiaffinities
| [1] | Cassier G, Mahzouli H. and Zeroiali E. H, Generalized Toeplitz operators and cyclic operators, Oper. Theor. Advances and Applications 153 (2004): 03-122. |
| [2] | Kubrusly C. S., An Introduction to Models and Decompositions in Operator Theory. Birkha ̈users, Boston, 1997. |
| [3] | Kubrusly C. S., Hilbert Space Operators, Birkha ̈users, Basel, Boston, 2003. |
| [4] | Lins B, Meade P, Mehl C and Rodman L. Normal Matrices and Polar decompositions in infinite Inner Products. Linear and Multilinear algebra, 49: 45-89, 2001. |
| [5] | Mehl C. and Rodman L. Classes of Normal Matrices in infinite Inner Products. Linear algebra Appl, 336: 71-98, 2001. |
| [6] | Mostafazadeh A., Pseudo-Hermiticity versus PT-symmetry, III, Equivalance of pseudo-Hermiticity and the presence of antilinear symmetries, J. Math. Phys. 43 (8) (2002), 3944-3951. |
| [7] | Nzimbi B. M, Pokhariyal G. P and Moindi S. K, A note on A-self-adjoint and A-Skew adjoint Operators, Pioneer Journal of Mathematics and Mathematical sciences, (2013), 1-36. |
| [8] | Nzimbi B. M, Pokhariyal G. P and Moindi S. K, A note on Metric Equivalence of Some Operators, Far East Journal of Mathematical sciences, Vol 75, No. 2 (2013), 301-318. |
| [9] | Nzimbi B. M., Khalagai J. M. and Pokhariyal G. P., A note on similarity, almost similarity and equivalence of operators, Far East J. Math. Sci. (FMJS) 28 (2) (2008), 305-317. |
| [10] | Nzimbi B. M, Luketero S. W, Sitati I. N, Musundi S. W and Mwenda E, On Almost Similarity and Metric Equivalence of Operators, Accepted to be published by Pioneer Journal of Mathematics and Mathematical sciences(June 14,2016). |
| [11] | Patel S. M., A note on quasi-isometries II Glasnik Matematicki 38 (58) (2003), 111-120. |
| [12] | Rehder Wulf, On the product of self-adjoint operators, Internat. J. Math. and Math. Sci 5 (4) (1982), 813-816. |
| [13] | Rudin W, Functional Analysis, 2nd ed., International Series in Pure and Applied Math., Mc Graw-Hill’s, Boston, 1991. |
| [14] | Suciu L, Some invariant subspaces of A-contractions and applications, Extracta Mathematicae 21 (3) (2006), 221-247. |
| [15] | Sz-Nagy B, Foias C, Bercovivi H and Kerchy L, Harmonic Analysis of Operators on Hilbert Space, Springer New York Dordrecht London (2010). |
| [16] | Tucanak M and Weiss G, Observation and Control for Operator Semi groups Birkhauser, Verlag, Basel, 2009. |
| [17] | Virtanen J. A: Operator Theory Fall 2007. |
| [18] | Yeung Y. H, Li C. K and L. Rodman, on H-unitary and Block Toeplitz H-normal operators, H-unitary and Lorentz matrices: A review, Preprint. |
APA Style
Isaiah N. Sitati. (2016). On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities. Mathematics and Computer Science, 1(3), 56-60. https://doi.org/10.11648/j.mcs.20160103.14
ACS Style
Isaiah N. Sitati. On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities. Math. Comput. Sci. 2016, 1(3), 56-60. doi: 10.11648/j.mcs.20160103.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.mcs.20160103.14,
author = {Isaiah N. Sitati},
title = {On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities},
journal = {Mathematics and Computer Science},
volume = {1},
number = {3},
pages = {56-60},
doi = {10.11648/j.mcs.20160103.14},
url = {https://doi.org/10.11648/j.mcs.20160103.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20160103.14},
abstract = {In this paper, we investigate properties of A-self-adjoint operators and other relations on Hilbert spaces. In this context, A is a self-adjoint and an invertible operator. More results on operator equivalences including similarity, unitary and metric equivalences are discussed. We also investigate conditions under which these classes of operators are self- adjoint and unitary. We finally locate their spectra.},
year = {2016}
}
TY - JOUR T1 - On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities AU - Isaiah N. Sitati Y1 - 2016/09/07 PY - 2016 N1 - https://doi.org/10.11648/j.mcs.20160103.14 DO - 10.11648/j.mcs.20160103.14 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 56 EP - 60 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20160103.14 AB - In this paper, we investigate properties of A-self-adjoint operators and other relations on Hilbert spaces. In this context, A is a self-adjoint and an invertible operator. More results on operator equivalences including similarity, unitary and metric equivalences are discussed. We also investigate conditions under which these classes of operators are self- adjoint and unitary. We finally locate their spectra. VL - 1 IS - 3 ER -
Information
Email: