| Peer-Reviewed

On A-Self-Adjoint, A-Unitary Operators and Quasiaffinities

Received: 8 August 2016     Accepted: 18 August 2016     Published: 7 September 2016
Views:       Downloads:
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.

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

Keywords

A-Self-Adjoint, A-Unitary, Hilbert Space, Metric Equivalence, Quasiaffinities

References
[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.
Cite This Article
  • 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

    Copy | Download

    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

    Copy | Download

    AMA 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

    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}
    }
    

    Copy | Download

  • 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  - 

    Copy | Download

Author Information
  • School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya

  • Sections