Unconditional basic sequence in $L^p({\mu})$ and its $l^p$-stability

This paper is concerned with unconditional basic sequences in $L^p(\mu )$. We prove that, under some conditions, a sequence in $L^p(\mu )$ is a bounded unconditional basic sequence if and only if it is $l^p$-stable. At last the results are applied to the shift-invariant basic sequences generated by a finite subset of $L^p(R^s)$, which is very important in wavelet analysis.