Volume 1, Issue 3, September 2016, Page: 56-60
On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities
Isaiah N. Sitati, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Received: Aug. 8, 2016;       Accepted: Aug. 18, 2016;       Published: Sep. 7, 2016
DOI: 10.11648/j.mcs.20160103.14      View  2281      Downloads  86
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.
Keywords
A-Self-Adjoint, A-Unitary, Hilbert Space, Metric Equivalence, Quasiaffinities
To cite this article
Isaiah N. Sitati, On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities, Mathematics and Computer Science. Vol. 1, No. 3, 2016, pp. 56-60. doi: 10.11648/j.mcs.20160103.14
Copyright
Copyright © 2016 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.
Reference
[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.
Browse journals by subject