Approximation of semigroups of isometries in a Hilbert space (Q1589174)

The class of approximating \(C_0\)-semigroups of isometrical operators \((U_t)_{t\geq 0}\) for a given \(C_0\)-semigroup \((V_t)_{t\geq 0}\) in a Hilbert space is introduced as satisfying the condition \[ \|U'_t-V'_t\|_2={\mathcal O}(t^{1/2}), \;t\to 0. \] Here \((U'_t)_{t\geq 0}\) and \((V'_t)_{t\geq 0}\) are minimal unitary dilations. Properties of approximating \(C_0\)-semigroups and their generators are investigated.