Volume 69 | Issue 3 | Year 2023 | Article Id. IJMTT-V69I3P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I3P501
Received | Revised | Accepted | Published |
---|---|---|---|
03 Feb 2023 | 05 Mar 2023 | 15 Mar 2023 | 27 Mar 2023 |
In this paper, we generalize metrically equivalent operators to the class of posimetrically equivalent operators. Some basic properties of this class are covered. We also relate this equivalence relation to the class of quasi-p-normal operators. We also relate this class to other equivalence relations such as n-metric equivalence.
[1] Benard Mutuku Nzimbi, and Stephen Wanyonyi Luketero, “On Unitary Quasi- Equivalence of Operators,” International
Journal of Mathematics and Its Applications, vol. 8, no. 1, pp. 207-215, 2020. [Google Scholar] [Publisher Link]
[2] D. Senthilkumar, and N. Revathi, “Quasi-P Normal and Quasi-n-P Normal Composition, Weighted Composition and Composite
Multiplication Operators,” International Journal of Scientific and Engineering Research, vol. 10, no. 1, pp. 951-954, 2019.
[Publisher Link]
[3] Eiman H. Abood, and Mustafa A. Al-loz, “ On Some Generalizations of (n,m)- Normal Powers Operators on Hilbert Space, ”
Journal of Progressive Research in Mathematics, vol. 7, no. 3, 2016.
[4] Adnan A.S. Jibril, “On Operators for which T ∗2
(T )
2 = (T ∗T )
2
,” International Mathematical Forum, vol. 5, no. 46, pp. 2255-
2262, 2010. [Publisher Link]
[5] A.A. Jibril, “On Almost Similar Operators,” Arabian Journal for science and Engineering, vol. 21, no. 3, pp. 443-449, 1996.
[6] Adnan Jibril, “On n-power Normal Operators,” The Arabian Journal for Science and Engineering, vol. 33, no. 2, pp. 247-251,
2008. [Publisher Link]
[7] K.M. Manikandan, and T. Veluchamy, “On (N+K) Power Class (Q) Operators in the Hilbert space-I,” International Journal
of Mathematics and Technology, vol. 55, no. 6, pp. 450-454, 2018. [Google Scholar] [Publisher Link]
[8] K.M. Manikandan, and T. Veluchamy, “On (N+K) Power Class(Q) Operators in the Hilbert Space-II,” International Journal
of Mathematics and Technology, vol. 55, no. 7, pp. 455-462, 2018. [CrossRef] [Google Scholar] [Publisher Link]
[9] Mahmoud Kutkut, “On Quasi-Equivalent Operators,” Bulletin of the Calcutta Mathematical Society, vol. 90, 1998.
[10] B.M. Nzimbi, G.P. Pokhariyal, and S.K. Moindi, “A Note on Metric Equivalence of some Operators,” Far East Journal of
Mathematical Sciences (FJMS), vol. 75, no. 2, pp. 301-318, 2013. [Google Scholar] [Publisher Link]
[11] Musundi S. Wabomba et al. , “ On Almost Similarity Operator Equivalence Relation,” International Journal of Recent
Research and Applied Studies, vol. 15, no. 3, pp. 293-299, 2013. [Google Scholar] [Publisher Link]
[12] Sadoon Ibrahim Othaman, “Nearly Equivalent Operators,” Mathematica Bohemica, vol. 121, no. 2, pp. 133-141, 1996.
[Google Scholar] [Publisher Link]
[13] S. Paramesh, D. Hemalatha, and V.J. Nirmala, “A Study On n-Power Class (Q)Operators,” International Research Journal of
Engineering and Technology, vol.6, no. 1, pp. 1729-1734, 2019. [Publisher Link]
[14] V.Revathi, and P. Maheswari Naik, “On Quasi-class (Q) Operator,” International Journal of Mathematics and Its Applications,
vol. 8, no. 2, pp. 49-65, 2020. [Publisher Link]
[15] V. Revathi, and P. Maheswari Naik, “A Study on Properties of M Quasi- Class (Q) Operator,” International Journal of
Advance Research, Ideas and Innovations in Technology, vol. 5, no. 5, pp. 387-390, 2019. [Google Scholar] [Publisher Link]
[16] Wanjala Victor, and Beatrice Adhiambo Obiero, “On N-A-Metrically Equivalent and A- Metrically Equivalent Operators, ”
International Journal of Mathematics and its Applications, vol. 9, no. 2, pp. 97-100, 2021. [Google Scholar] [Publisher Link]
[17] Wanjala Victor, and Beatrice Adhiambo Obiero, “On Almost Class (Q) and Class (M,n) Operators,” International Journal of
Mathematics and its Applications, vol. 9, no. 2, pp. 115-118, 2021. [Google Scholar] [Publisher Link]
[18] Wanjala Victor, and A.M. Nyongesa, “On (α, β) - class(Q) Operators,” International Journal of Mathematics and its Applications,
vol. 9, no. 2, pp. 111-113, 2021. [Google Scholar] [Publisher Link]
[19] Wanjala Victor, and Peter Kiptoo Rutto, “On K∗ Quasi-n-Class (Q) Operators,” International Journal of Mathematics and Its
Applications, vol. 9, no. 2, pp. 189-193, 2021. [Google Scholar] [Publisher Link]
[20] Wanjala Victor, and A.M. Nyongesa, “On Class (Q∗) Operators,” International Journal of Mathematics and its Applications,
vol. 9, no. 2, pp. 227-230, 2021. [Publisher Link]
[21] Wanjala Victor, and A.M. Nyongesa, “Further Generalization of Unitary Quasi- Equivalence of Operators,” International
Journal of Mathematics and its Applications, vol. 9, no. 2, pp. 223-225, 2021. [Google Scholar] [Publisher Link]
[22] Wanjala Victor et al., “On Skew Quasi-p-class (Q) Operators,” International Journal of Mathematics and Its Applications, vol.
11, no. 1, pp. 65-74, 2023. [Google Scholar] [Publisher link]
[23] Wanjala Victor, and Beatrice Adhiambo Obiero, “On class (BQ) Operators,” Global Journal of Advanced Research, vol. 8, no.
4, pp. 118-120, 2021. [Publisher Link]
[24] Wanjala Victor, A.M. Nyongesa, and John Wanyonyi Matuya, “On Metric Equivalence of Operators of Order N,” International
Journal of Statistics and Applied Mathematics, vol. 7, no. 1, pp. 94-97, 2022. [CrossRef] [Google Scholar]
[25] Wanjala Victor, and A.M. Nyongesa, “On (n,m) - Metrically Equivalent Operators,” International Journal of Mathematics and
its Applications, vol. 9, no. 2, pp. 101-104, 2021. [Google Scholar] [Publisher Link]
[26] Wanjala Victor, R.K. Obogi, and M.O. Okoya, “On N-Metric Equivalence of Operators,” International Journal of Mathematics
and its Applications, vol. 8, no. 1, pp. 107-109, 2020. [Google Scholar] [Publisher Link]
Wanjala Victor, John Wanyonyi Matuya, Edward Njuguna, "On Posimetrically Equivalent Operators," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 3, pp. 1-6, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I3P501