Geodesic
On a~weak topology for Hadamard spaces
Sbornik. Mathematics, Tome 214 (2023) no. 10, pp. 1373-1389

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We investigate whether the existing notion of weak sequential convergence in Hadamard spaces can be induced by a topology. We provide an affirmative answer in what we call weakly proper Hadamard spaces. Several results from functional analysis are extended to the setting of Hadamard spaces. Our weak topology coincides with the usual one in the case of a Hilbert space. Finally, we compare our topology with other existing notions of weak topologies. Bibliography: 24 titles.
Keywords: weak convergence, weak topology
Mots-clés : Hadamard space. 
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     author = {A. B{\cyryo}rd{\cyryo}llima},
     title = {On a~weak topology for {Hadamard} spaces},
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A. Bёrdёllima. On a~weak topology for Hadamard spaces. Sbornik. Mathematics, Tome 214 (2023) no. 10, pp. 1373-1389. http://geodesic.mathdoc.fr/item/SM_2023_214_10_a1/