Bohr compactification of separable locally convex spaces

It is not well-known that for each separable real locally convex space, its Bohr compactification is isomorphic as a topological group to the Bohr compactification of the topological group $ \mathbb{R} $ of all real numbers. This is the case for each separable real Banach space. In this expository...

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Main Author: Sidney A. Morris
Format: Article
Language:English
Published: AIMS Press 2025-03-01
Series:Electronic Research Archive
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Online Access:https://www.aimspress.com/article/doi/10.3934/era.2025060
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author Sidney A. Morris
author_facet Sidney A. Morris
author_sort Sidney A. Morris
collection DOAJ
description It is not well-known that for each separable real locally convex space, its Bohr compactification is isomorphic as a topological group to the Bohr compactification of the topological group $ \mathbb{R} $ of all real numbers. This is the case for each separable real Banach space. In this expository research note, we state the results explicitly and provide accessible proofs.
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spelling doaj-art-5d4e93de6433474c8fb393cb1166ea732025-08-20T02:08:24ZengAIMS PressElectronic Research Archive2688-15942025-03-013331333133610.3934/era.2025060Bohr compactification of separable locally convex spacesSidney A. Morris0Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Victoria 3086, AustraliaIt is not well-known that for each separable real locally convex space, its Bohr compactification is isomorphic as a topological group to the Bohr compactification of the topological group $ \mathbb{R} $ of all real numbers. This is the case for each separable real Banach space. In this expository research note, we state the results explicitly and provide accessible proofs.https://www.aimspress.com/article/doi/10.3934/era.2025060bohr compactificationabelian topological groupbanach spacepontryagin dualitydual groupseparable locally convex space
spellingShingle Sidney A. Morris
Bohr compactification of separable locally convex spaces
Electronic Research Archive
bohr compactification
abelian topological group
banach space
pontryagin duality
dual group
separable locally convex space
title Bohr compactification of separable locally convex spaces
title_full Bohr compactification of separable locally convex spaces
title_fullStr Bohr compactification of separable locally convex spaces
title_full_unstemmed Bohr compactification of separable locally convex spaces
title_short Bohr compactification of separable locally convex spaces
title_sort bohr compactification of separable locally convex spaces
topic bohr compactification
abelian topological group
banach space
pontryagin duality
dual group
separable locally convex space
url https://www.aimspress.com/article/doi/10.3934/era.2025060
work_keys_str_mv AT sidneyamorris bohrcompactificationofseparablelocallyconvexspaces