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

Miroslav Bačák

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Submission date: 01. Feb. 2013
Pages: 12
published in: Communications in contemporary mathematics, 16 (2014) 6, art-no. 1350044 
DOI number (of the published article): 10.1142/S0219199713500442
Bibtex
MSC-Numbers: 47H20, 58D07
Keywords and phrases: gradient flow semigroup, Lie-Trotter-Kato formula, resolvent
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Abstract:
The Lie-Trotter-Kato product formula was recently extended into Hadamard spaces by [Stojkovic, Adv. Calc. Var., 2012]. The aim of our short note is to give a simpler proof relying upon weak convergence. Unlike in the original proof, we completely avoid using ultrapowers of Hadamard spaces and any additional compactness assumptions.