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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On orthogonally exponential
and orthogonally additive mappings


Author: Janusz Brzdek
Journal: Proc. Amer. Math. Soc. 125 (1997), 2127-2132
MSC (1991): Primary 39B52
MathSciNet review: 1376751
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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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Additional Information

Janusz Brzdek
Affiliation: Department of Mathematics, Pedagogical University, Rejtana 16 A, 35-310 Rzeszow, Poland

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03791-X
PII: S 0002-9939(97)03791-X
Keywords: Baire measurability, Christensen measurability, orthogonal additivity, orthogonally exponential functional.
Received by editor(s): September 8, 1995
Received by editor(s) in revised form: February 8, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society