Functions operating from a complex Banach space to its real part

Briem, Eggert

doi:10.1090/S0002-9939-97-03655-1

Functions operating from a complex Banach space to its real part
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Proc. Amer. Math. Soc. 125 (1997), 861-867 Request permission

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$B=C_ { \mathbf {R}}(X)$.

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