Quasi-Sectorial Contractions and Operator-Norm Convergence

Quasi-sectorial contractions play important rôle throughout this book. We need this type of mappings in different parts of the text, but mainly in the Part III: Trotter-Kato product formula for non-self-adjoint semigroups. For quasi-sectorial contractions we can improve the original Chernoff \(\sqrt {n}\) -Lemma up to the \((\sqrt [3]{n})^{-1}\) - Lemma estimate in the Chernoff-Lemma operator-norm topology, as well as to uplift to this topology the convergence of the corresponding product formulæ.