Let X=(X(n))_{n ∈ Z+} be a standard subproduct system of C*-correspondences over a C*-algebra M. Let T=(T_n)_{n ∈ Z+} be a pure completely contractive, covariant representation of X on a Hilbert space H. If S is a closed subspace of H, then S is invariant for T if and only if there exist a Hilbert space D, a representation π of M on D, and a partial isometry Π: F_X⊗_πD→ H such that Π (S_n(ζ)⊗ I_D)=T_n(ζ)Π    (ζ∈ X(n), n ∈ Z₊), and S = ran Π, or equivalently, P_S=ΠΠ*. This result leads us to a list of consequences including Beurling-Lax-Halmos type theorem and other general observations on wandering subspaces. We extend the notion of curvature for completely contractive, covariant representations and analyze it in terms of the above results.

The research of Sarkar was supported in part by (1) National Board of Higher Mathematics (NBHM), India, grant NBHM/R.P.64/2014, and (2) Mathematical Research Impact Centric Support (MATRICS) grant, File No : MTR/2017/000522, by the Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India. Trivedi thanks Indian Statistical Institute Bangalore for the visiting scientist fellowship. Veerabathiran was supported by DST-Inspire fellowship.