Fibers of $L^{\infty}$ algebra

Details Fibers of $L^{\infty}$ algebra Fibers of $L^{\infty}$ algebra

2010-06-30

arxiv.org/abs/1006.5900v3

Mathematics

Functional Analysis

4 pages

Scientific paper

It is shown that Gelfand transforms of elements $f\in\lmu$ are constant at
almost every fiber $\Pi^{-1}(\{x\})$ of the spectrum of $\lmu$ in the following
sense: for each $f\in\lmu$ there is an open dense subset $U=U(f)$ of this
spectrum having full measure and such that the Gelfand transform of $f$ is
constant on the intersection $\Pi^{-1}(\{x\})\cap U$.

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