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In this article we survey results concerning asymptotic properties of C0-semigroups on Banach spaces with respect to the weak operator topology. The property " no eigenvalues of the generator on the imaginary axis " is equivalent to weak stability for most time values; a phenomenon called " almost weak stability ". Further, sufficient conditions implying(More)
We give conditions on a strongly continuous semigroup T and a bounded operator B, such that the perturbed semigroup inherits the regularity properties of T. 1. Introduction The aim of this paper is to understand why some regularity properties of strongly continuous semigroups persist under bounded perturbation while others do not. This is a very old(More)
In this paper, we present two quite general approximation theorems for the propagators of higher order (in time) abstract Cauchy problems, which extend largely the classical Trotter-Kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions. Then, we apply the approximation theorems to deal with the second(More)