In this talk I first present my recent work on a perturbation problem of the shift semigroup of L 2 (0,∞). Then I discuss its application to E0-semigroups, which is a joint work with R. Srinivasan. I show that there exist uncountably many mutually non-cocycle conjugate type III E0-semigroups with the same Tsirelson invariant as that of CCR flow of index 1. These examples are distinguished by the type of the associated von Neumann algebras A(U), where U is a bounded open subset of the half-line.