abstract The notion of invariant subspaces is useful in a number of theoretical and practical applications. In this paper we give an elementary treatment of invariant subspaces that stresses their connection with simple eigenvalues and their eigenvectors.

z on the classical Hardy space H. Though there are many aspects of this operator worthy of study [20], we will focus on the description of its invariant subspaces by which we mean the closed linear manifolds E ⊂ H for which BE ⊂ E . When 1 < p < ∞, a seminal paper of Douglas, Shapiro, and Shields [8] describes these invariant subspaces by using the important concept of a pseudocontinuation deve...