The Index Of Quasi-invariant Subspaces In Banach Spaces Of Analytic Functions Over The Complex Plane

In this paper, we list general conditions on Banach spaces of analytic functions over the complex plane implying the existence of quasi-invariant subspaces of arbitrary index, and use lacunary power series to prove its correctness. As application, we also describe that the Fock-type space and Hilbert space contain quasi-invariant subspaces of arbitrary index.