On the Topology of Invariant Subspaces of a Shift of Higher Multiplicity

Following Beurling’s theorem R. Douglas and C. Pearcy have studied topology of invariant subspace lattice. R.Yang offered a description of path connected components of invariant subspace lattice for shift of multiplicity one. This paper generalizes the result to arbitrary finite multiplicity. We show that there exists a one to one correspondence between the invariant subspace lattice of shift of arbitrary finite multiplicity and the space of inner functions.