Large Bergman Spaces and The Berezin Transform on the Toeplitz Algebra

Abstract

In wide class of weighted Bergman spaces , we construct inevitable non-cyclic elements ,these are then used to produce z- invariant sub spaces of index higher than one generated non trivial bilaterally invariant subspaces in a nti symmetricallyweighted Hilbert Spaces of sequences .We also study the boundary behavior of the Berezin transform on C*-algebra generated analytic Toeplitz operators on the Bergaman Spaces.