On $(n,m)$-Metrically Equivalent Operators

# Wanjala Victor1 and A. M. Nyongesa1

1Department of Mathematics and Computing, Rongo University, Kitere Hills, Kenya.

Abstract: In this paper, we introduce the class of (n,m)-metrically equivalent operators which is a generilazation of metrically equivalent operators and n-metrically equivalent operators. We then look at some properties of this class and its relation to some higher classes like quasi-isometries and the (n,m)-class (Q) operators. we also look at the relationship between this class and other equivalence relations like metrically equivalent and n-metrically equivalent operators.
Keywords: (n,m)-metrically equivalent, n-metrically equivalent, metrically equivalent, (n,m)-class(Q), normal and n-normal operators.

Cite this article as: Wanjala Victor and A. M. Nyongesa, On $(n,m)$-Metrically Equivalent Operators, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 101-104.

References
1. 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, 7(3)(2016), 1063-1070.
2. A. A. Jibril, On n-power normal operators, The Arabian Journal for Science and Engineering, 33(2008), 247-251.
3. B. M. Nzimbi, G. P. Pokhariyal and S. K. Moindi, A Note on Metric Equivalence of some Operators, Far East J.F Math. Sci. (FJMS), 75(2013), 301-318.
4. S. A. Alzuraiqi and A. B. Patel, On n-Normal Operators, General mathematics Notes, 1(2)(2010), 61-73.
5. Wanjala Victor, R. K. Obogi and M. O. Okoya, On N-Metric equivalence of Operators, International Journal of Mathematics And its Applications, 8(1)(2020), 107-109.

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