Backward shift invariant subspaces in reproducing kernel Hilbert spaces - Fricain, Emmanuel; Mashreghi, Javad; Rupam, Rishika (MATHEMATICA SCANDINAVICA, 2020)
In this note, we describe the backward shift invariant subspaces for an abstract class of reproducing kernel Hilbert spaces. Our main result is inspired by a result of Sarason concerning de Branges-Rovnyak spaces (the non-extreme case). Furthermore, we give new applications in the context of the range space of co-analytic Toeplitz operators and sub-Bergman spaces.