Refined scales of decaying rates of operator semigroups on Hilbert spaces: typical behaviour

Abstract

We study relations between the decaying rates of operator semigroups on Hilbert spaces and some spectral properties of their respective generators; in particular, we show that the decaying rates of orbits of semigroups which are stable but not exponentially stable, typically in Baire's sense, depend on sequences of time going to infinity.

15 pages, to appear in Proceedings of the American Mathematical Society. Improved exposition. Major changes following suggestions of the referee