Volume 2, Issue 6, November 2017, Page: 79-88
On Some n-Involution and k-Potent Operators on Hilbert Spaces
Bernard Mutuku Nzimbi, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Beth Nyambura Kiratu, Department of Pure and Applied Mathematics, Faculty of Applied Sciences and Technology, Technical University of Kenya, Nairobi, Kenya
Stephen Wanyonyi Luketero, School of Mathematics, College of Biological and Physical Sciences, University of Nairobi, Nairobi, Kenya
Received: May 15, 2017;       Accepted: Jun. 3, 2017;       Published: Nov. 14, 2017
DOI: 10.11648/j.mcs.20170206.11      View  1933      Downloads  114
Abstract
In this paper, we survey various results concerning -involution operators and -potent operators in Hilbert spaces. We gain insight by studying the operator equation , with where . We study the structure of such operators and attempt to gain information about the structure of closely related operators, associated operators and the attendant spectral geometry. The paper concludes with some applications in integral equations.
Keywords
n-Involution, Idempotent, Spectral Radius, Twist, Invection, Q-Equivalence
To cite this article
Bernard Mutuku Nzimbi, Beth Nyambura Kiratu, Stephen Wanyonyi Luketero, On Some n-Involution and k-Potent Operators on Hilbert Spaces, Mathematics and Computer Science. Vol. 2, No. 6, 2017, pp. 79-88. doi: 10.11648/j.mcs.20170206.11
Copyright
Copyright © 2017 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]
S. Furtado, Products of two involutions with prescribed eigenvalues and some applications, Linear Algebra and its Applications, 429(2008), 1663-1678.
[2]
T. Furuta, Invitation to linear operators: from matrices to bounded linear operators on a Hilbert space, Taylor Francis, London, 2001.
[3]
M. I. Kadets and K. E. Kaibkhanov, Continuation of a linear operator to an involution, Mathematical Notes 61, No. 5 (1997), 560–565.
[4]
Nikolai Karapetiants and Stefan Samko, Equations with involutive operators, Springer Science + Business Media, LLC, New York, 2001.
[5]
C. S. Kubrusly, An introduction to models and decompositions in operator theory, Birkh¨auser, Boston, 1997.
[6]
Mao-Lin Liang and Li-Fang Dai, The solvability conditions of matrix equations with involutions, Electronic Journal of Linear Algebra, Vol. 22 (2011), 1138-1147.
[7]
B. M. Nzimbi, G. P. Pokhariyal, and S. K. Moindi, A note on metric equivalence of some operators, Far East J. of Math. Sci. (FJMS) 75, No. 2 (2013), 301–318.
[8]
S. K. Singh, G. Mukherjee, and M. Kumar Roy, -range, -range of operators in a Hilbert space, International J. of Engineering and Sciences (IJES) 3, Issue 8 (2014), 26–35.
[9]
T. Yongge, A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications, Linear and Multilinear Algebra, Vol. 59, No. 11(2011), 1237-1246.
[10]
C. Xu, On the idempotency, involution and nilpotency of a linear combination of two matrices, Linear and Multilinear Algebra, Vol. 63, No. 8(2015), 1664-1677.
Browse journals by subject