Bands in $L_p$-spaces

Hendrik Vogt, Jürgen Voigt

Published 2016-03-24Version 1

For a general measure space $(\Omega,\mu)$, it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu'+\mu"$ such that $M=L_p(\mu')=\{f\in L_p(\mu);f=0\ \mu"\text{-a.e.}\}$. The theory is illustrated by an example, with an application to absorption semigroups.