Let X=(X(n))n ∈ Z+ be a standard subproduct systemof C*-correspondences over a C*-algebra M. LetT=(Tn)n ∈ Z+ be a pure completely contractive,covariant representation of X on a Hilbert space H. IfS is a closed subspace of H, thenS is invariant for T if and only if there exist aHilbert space D, a representation π of Mon D, and a partial isometry Π:FX?πD→ H such thatΠ (Sn(ζ)? ID)=Tn(ζ)Π ??(ζ∈ X(n), n ∈ Z+),and S = ran Π, or equivalently, PS=ΠΠ*. This result leads us to a list of consequencesincluding Beurling-Lax-Halmos type theorem and other general observations onwandering subspaces. We extend the notion of curvature forcompletely contractive, covariant representations and analyze it interms of the above results.
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