  We show that one-dimensional circle is the only case for closed smooth metric
measure spaces with nonnegative Bakry-\'{E}mery Ricci curvature whose spectrum
of the weighted Laplacian has an optimal positive upper bound. This result
extends the work of Hang-Wang in the manifold case (Int. Math. Res. Not. 18
(2007), Art. ID rnm064, 9pp).
