Bohr compactification of separable locally convex spaces

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Abstract

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 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.

Keywords

Bohr compactification / abelian topological group / Banach space / Pontryagin duality / dual group / separable locally convex space

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