Annihilating a subspace of $L_1$ with the sign of a continuous function
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Abstract:
Let $(X,\Sigma , \mu )$ be a $\sigma$-finite, nonatomic, Baire measure space. Let $G$ be a finite dimensional subspace of $L_1(X,\Sigma , \mu )$. There is a bounded, continuous function, $q$, defined on $X$, such that (1) $\int _X g\operatorname {sgn} q d\mu =0$ for all $g \in G$, and (2) $|\operatorname {sgn} q | =1$ almost everywhere.References
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Additional Information
- Daniel Wulbert
- Affiliation: Mathematics Department 0112, University of California, San Diego, La Jolla, California 92093
- Email: dwulbert@ucsd.edu
- Received by editor(s): May 28, 1998
- Received by editor(s) in revised form: September 25, 1998
- Published electronically: November 24, 1999
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2431-2438
- MSC (1991): Primary 46E30; Secondary 46G10, 26A15
- DOI: https://doi.org/10.1090/S0002-9939-99-05317-4
- MathSciNet review: 1662234