Toeplitz properties of $\omega$-order preserving partial contraction mapping

Akinola Yussuff     Akinyele; Jude  Babatunde Omosowon; Moses Adebowale Aasa; Bayo Musa Ahmed; Kareem Akanbi Bello

doi:10.26637/mjm1002/002

Abstract

In this paper, spectral mapping theorem for the point spectrum on infinitesimal generator of a $C_0$-semigroup was further investigated. Toeplitz properties of semigroup considering $\omega$-order preserving partial contraction mapping ($\omega-OCP_n$) as a semigroup of linear operator was established to obtained new results. We also consider $A\in \omega-OCP_n$ which is the infinitesimal generator of a $C_{0}$-semigroup using the Spectral Mapping Theorem (SMT) to obtain the relationships between the spectrum of $A$ and the spectrum of each of the operators $\{T(t),~t\ge 0\}$.

Keywords:

$\omega-OCP_n$ , $C_{0}$-semigroup, Spectrum, Toeplitz matrix

Mathematics Subject Classification:

06F15, 06F05, 20M0

Authors Imprint References Funding Related Articles Downloads

Akinola Yussuff Akinyele Department of Mathematics, University of Ilorin, Ilorin, Nigeria.
Jude Babatunde Omosowon West Virginia University, Morgantown, West Virginia, USA
Moses Adebowale Aasa Oyo State College of Education, Lanlate, Nigeria
Bayo Musa Ahmed University of Ilorin, Ilorin, Nigeria https://orcid.org/0009-0000-9828-5232
Kareem Akanbi Bello University of Ilorin, Ilorin, Nigeria

Pages: 119-127
Date Published: 01-04-2022
Vol. 10 No. 02 (2022): Malaya Journal of Matematik (MJM)

A. V. Balakrishnan, An Operator Calculus for Infinitesimal generators of Semigroup, Trans Amer. Math. Soc, 91(1959), 330-353.

S. BANACh,, Surles Operation Dam Les Eusembles Abstracts et lear Application Aus Equation integrals, Fund. Math., 3(1922), 133-181.

A. W. BOJANCZyK, R. P. BrEnt, F. R. DE Hoog, AND D. R. SwEEt, On the stability of the Bareiss and related Toeplitz factorization algorithms SIAM Journal on Matrix Analysis and Applications, 16(1995), 40-57.

A. Böttcher, And S. M. Grudsky,Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis Birkhäuser, (2012). ISBN 978-3-0348-8395-5.

K. Engel, And R. Nagel, One-parameter Semigroups for Linear Equations, Graduate Texts in Mathematics, 194, Springer, New York, (2000).

G. Greiner, J. Voigt, And M. Wolf, On the Spectral Bond Generator of Semigroups of Positive Operators, J. Operator, 5(1981), 245-256.

M. Hasegawa, On the Convergence of Resolvents of Operators Pacific Journal of Mathematics, 21(1967), $35-47$.

J. V. Neerven, The Asymptotic Beahavior of Semigroup of Linear Operators. Mathematisches Institut Auf der Morgenstelle 10, D-720276 Tübingen, Germany, (1996).

A. Pazy, Semigroup of Linear Operators And Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer Verlag, New York, Berlin Heidelberg, Tokyo, (1983).

K. RAUF AND A. Y. AKINYELE, Properties of $omega$-order preserving partial contraction mapping and its relation to $C_0$-semigroup, International Journal of Mathematics and Computer Science, 14(1) (2019), 61-68.

K. Rauf, A. Y. Akinyele, M. O. Etuk, R. O. Zubair and M. A. Aasa, Some result of stability and spectra properties on semigroup of linear operator, Advances in Pure Mathematics, 9(2019), 43-51.

M. Slemrod, Asymptotic Behaviour of $C_0$-semigroup as Determined by the Spectrum of the Generator, Indiana Univ. Math. J., 25(1976), 783-792.

I. I. Vrabie,, $C_0$-semigroup And Application , Mathematics Studies, 191, Elsevier, North-Holland, (2003).

K. Yosida, On the differentiability and representation of one-parameter semigroups of linear operators, $J$. Math. Soc., 1(1948), 15-21.