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Functions operating from a complex Banach space to its real part

Author: Eggert Briem
Journal: Proc. Amer. Math. Soc. 125 (1997), 861-867
MSC (1991): Primary 46E15, 46J10
MathSciNet review: 1363450
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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 $|b|\in {\rm Re}B$ for all $b$ in an ultraseparating Banach function space $B$, then Re$B=C_ { \mathbf {R}}(X)$.

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Additional Information

Eggert Briem
Affiliation: Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland

Keywords: Operating functions, function space, ultraseparation
Received by editor(s): March 9, 1995
Received by editor(s) in revised form: October 4, 1995
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society