A new proof of the Lie–Trotter–Kato formula in Hadamard spaces

The Lie–Trotter–Kato product formula has been recently extended into Hadamard spaces by Stojkovic [Approximation for convex functionals on non-positively curved spaces and the Trotter–Kato product formula, Adv. Calc. Var. 5 (2012) 77–216]. The aim of our short note is to give a simpler proof relying upon weak convergence instead of an ultrapower technique.