Abstract. In this paper, we study closed invariant subspaces under the action of a unilateral shift and a truncated shift in the Hardy space that takes values in a two-dimensional Hilbert space. We deal with characteristic functions, unitary equivalence and $C^{\ast }$-algebras on these spaces.

AMS Subject Classification (1991): 47B38, 47B35

Keyword(s): vector valued Hardy spaces and shift operators

Received October 19, 2005, and in final form May 4, 2007. (Registered under 6458/2009.)