On orthogonally exponential and orthogonally additive mappings

Brzdek, Janusz

doi:10.1090/S0002-9939-97-03791-X

On orthogonally exponential and orthogonally additive mappings
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by Janusz Brzdek

Proc. Amer. Math. Soc. 125 (1997), 2127-2132

DOI: https://doi.org/10.1090/S0002-9939-97-03791-X

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Abstract:

Let $E$ be a real inner product space, $(F,+)$ an abelian $\sigma$-bounded topological group, and $K$ a discrete subgroup of $F$. It is proved that (under suitable assumptions on $E)$ the Christensen and Baire measurable orthogonally additive functions $g\colon E\to F/K$ have particular selections. In consequence, descriptions of measurable orthogonally exponential complex functionals on $E$ are obtained.

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