Infinitesimal Generator of Mean Ergodic Theorem in Semigroup of Linear Operator

Akinola Yussuff Akinyele, Ajisope Michael Oyelami, Ohigweren Airenoni Uwaheren

Abstract


In this paper, results of Ergodic Theorem were obtained by investigating the behavior of $\omega$-order reversing partial contraction mapping (semigroup of linear operator) as $t$ tends to $+\infty$ of the means $\frac{1}{t}\int_{0}^{t}T(s)ds$ of a $C_0$-Semigroup of contraction $\{T(t);t \geq 0\}$ and it was shown that the infinitesimal generator of a $C_0$-Semigroup of contraction $\{T(t);t \geq 0\}$ is densely defined, linear, closed, reflexive and there exists a continuous bounded function.

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