Results of semigroup of linear operators in extrapolation spaces

Abstract

Results of an omega-order preserving partial contraction mapping (omega-OCPn) in generalized spaces are presented in this study. Assumed to be a closed linear operator on a Banach space X with a non-empty resolvent set rho(A) is A in omega-OCPn. If A is densely defined, the extrapolation spaces X-1 and X-1 will be associated with A in agreement. However, X-1 is a proper closed subspace of X-1 if A is not densely defined. Then, we demonstrated that the reason these spaces exist is because (X*)-1 and D(A0) are naturally isomorphic to (X*)-1 and (X*)-1, respectively.