Let W be a region in the complex plane. In this paper we introduce a class of sesquianalytic reproducing kernels on W that we call B-kernels. When W is the open unit disk D and certain natural additional hypotheses are added we call such kernels k Bergman-type kernels. In this case the associated reproducing kernel Hilbert space H(k) shares certain properties with the classical Bergman space L 2 a of the unit disk. For example, the weighted Bergman kernels
a , where the inclusion maps are contractive, and M z , the operator of multiplication with the identity function z, defines a contraction operator on H(k). Our main results about Bergman-type kernels k are the following two: First, once properly normalized, the reproducing kernel for any nontrivial zero based invariant subspace M of H(k) is a Bergman-type kernel as well. For the weighted Bergman kernels k b this result even holds for all M z -invariant subspace M of index 1, i.e., whenever the dimension of M/zM is one. Second, if M is any multiplier invariant subspace of H(k), and if we set C g =M ฤฑ zM, then M z | M is unitarily equivalent to M z acting on a space of C g -valued analytic functions with an operator-valued reproducing kernel of the type
where V is a contractive analytic function V: D Q L(E, C g ), for some auxiliary Hilbert space E. Parts of these theorems hold in more generality. Corollaries include contractive divisor, wandering subspace, and dilation theorems for all Bergman-type reproducing kernel Hilbert spaces. When restricted to index one invariant subspaces of H(k b ), 1 [ b [ 2, our approach yields new proofs of the contractive divisor property, the strong contractive divisor property, and the wandering subspace theorems and inner-outer factorization. Our proofs are based on the properties of reproducing kernels, and they do not involve the use of biharmonic Green functions as had some of the earlier proofs.