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

Abstract

In this paper, spectral mapping theorem for the point spectrum on infinitesimal generator of a C0-semigroup was further investigated. Toeplitz properties of semigroup considering ω-order preserving partial contraction mapping (ω − OCPn) as a semigroup of linear operator was established to obtained new results. We also consider A ∈ ω − OCPn which is the infinitesimal generator of a C0-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 ≥ 0}.