Operator-norm Trotter product formula on Banach spaces

Abstract: In this paper we collect results concerning the {operator-norm} convergent {Trotter} product formula for two semigroups ${\e^{- t A}}{t\geq 0}$, ${\e^{- t B}}{t\geq 0}$, with densely defined generators $A$ and $B$ in a {Banach} space. Although the {strong} convergence in Banach space for contraction semigroups is known since the seminal paper by Trotter (1959), which after more than three decades was extended to convergence in the {operator-norm} topology in {Hilbert} spaces by Rogava (1993), the {operator-norm} convergence in a {Banach} space was established only in (2001).