  In this paper we study complete manifolds equipped with smooth measures whose
spectrum of the weighted Laplacian has an optimal positive lower bound and the
$m$-dimensional Bakry-\'Emery Ricci curvature is bounded from below by some
negative constant. In particular, we prove a splitting type theorem for
complete smooth measure manifolds that have a finite weighted volume end. This
result is regarded as a study of the equality case of an author's theorem (J.
Math. Anal. Appl. 361 (2010) 10-18).
