Bands in $L_p$-spaces

Abstract

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

References in corpus (1)

• A note on absorption semigroups and regularity

Cited by in corpus (1)

• Atoms and associated spectral properties for positive operators on L^p