A Detail in the Proof of the Exponential Formulaof Operator Semigroups
Lianping Zhang · Journal of Shanxi University · 2002
There is a famous exponential formula in the theory of semigroups of bounded linear operators.To obtain the exponential formula,it must be proved that\{lim\}n→∞n\+\{n+1\}n!∫\+\{+∞\}\-0(ve\+\{-v\})\+n[T(vt)x-T(t)x]dv=0.But some books on the theory of semigroups of bounded linear operators have a detail mistake in the proof of the above limit formula.In this paper we point out the mistake and correct it.