On a weak topology for Hadamard spaces

Arian Bërdëllima

Published 2022-04-04Version 1

We investigate whether existing notions of weak sequential convergence on Hadamard spaces can be topologized, that is whether there exist corresponding notions of weak topologies. We provide an affirmative answer on what we call weakly proper Hadamard spaces. A notion of dual space is proposed and it is shown that our weak topology and dual space coincide with the standard ones in the case of a Hilbert space. We extend several results from classical functional analysis to the setting of Hadamard spaces, and we compare our topology to existing notions of weak topologies.