Functions operating from a complex Banach space to its real part
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Abstract:
We consider functions operating from a complex Banach function space to its real part. We show among other things, that if $|b|\in \textrm {Re}B$ for all $b$ in an ultraseparating Banach function space $B$, then Re$B=C_ { \mathbf {R}}(X)$.References
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Additional Information
- Eggert Briem
- Affiliation: Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland
- Email: briem@rhi.hi.is
- Received by editor(s): March 9, 1995
- Received by editor(s) in revised form: October 4, 1995
- Communicated by: Theodore W. Gamelin
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 861-867
- MSC (1991): Primary 46E15, 46J10
- DOI: https://doi.org/10.1090/S0002-9939-97-03655-1
- MathSciNet review: 1363450