We initiate the study of vector-valued sub-Bergman spaces on the unit disk, which are de Branges–Rovnyak subspaces of the vector-valued weighted Bergman space \({A}_{\alpha , E}^{2}\) , defined by the contractions \(T_{B}\) or \(T_{B}^{*}\) for an analytic multiplier B of \({A}_{\alpha ,E}^{2}\) . There are notable differences between the scalar and vector-valued cases, especially when E is infinite-dimensional. Throughout this work, we fill in some gaps and provide unified proofs for several results from the scalar case. Most of our proofs are more elementary and straightforward.
