On the topology of invariant subspaces of a shift of higher multiplicity

Abstract

Following Beurling's theorem and a study of the topology of invariant subspaces by R. Douglas and C. Pearcy description of path connected components of invariant subspace lattice for shift of multiplicity one has been given by R.Yang. This paper generalizes result to arbitrary finite multiplicity. We show that there exists one to one correspondence between the invariant subspace lattice of shift of arbitrary finite multiplicity and the space of inner functions.