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Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces
Abstract : We study the horofunction boundaries of Hilbert and Thompson geome-tries, and of Banach spaces, in arbitrary dimension. By comparing the boundaries of these spaces, we show that the only Hilbert and Thompson geometries that are isometric to Banach spaces are the ones defined on the cone of positive continuous functions on a compact space.
Cited literature [20 references]
https://hal.inria.fr/hal-01249343
Contributor : Cormac Walsh <>
Submitted on : Thursday, December 31, 2015 - 5:40:58 PM
Last modification on : Tuesday, December 8, 2020 - 10:34:21 AM
Long-term archiving on: : Tuesday, April 5, 2016 - 1:50:02 PM
Contributor : Cormac Walsh <>
Submitted on : Thursday, December 31, 2015 - 5:40:58 PM
Last modification on : Tuesday, December 8, 2020 - 10:34:21 AM
Long-term archiving on: : Tuesday, April 5, 2016 - 1:50:02 PM
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combined_infinite.pdf
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