Spectrum of Weighted Composition Operators. Part II. Weighted   composition operators on subspaces of Banach lattices
  We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not limited to) weighted isometries of Hardy spaces on the polydisk and unit ball in $\mathds{C}^n$. 
Arkady Kitover
math.FA