Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T1f...., Tn−1f) : f ∈ D} be an invariant graph subspace for M(H). Here n ≥ 2, D ⊆ H is a vector-subspace, Ti : D → H are linear transformations that commute with each multiplication operator Mφ ∈ M(H), and M is closed in H. In this paper we investigate the existence of nontrivial common invariant subsp...

Bounded operators with no non-trivial closed invariant subspace have been constructed by P. Enflo [6]. In fact, there exist bounded operators on the space 1 with no non-trivial closed invariant subset [12]. It is still unknown, however, if such operators exist on reflexive Banach spaces, or on the separable Hilbert space. The main result of this note (Theorem 1) asserts that the existence of an...

In this paper we study the Hilbert space of analytic functions with finite Dirichlet integral in a connected open set C2 in the complex plane. We show that every such function can be represented as a quotient of two bounded analytic functions, each of which has a finite Dirichlet integral. This has several consequences for the structure of invariant subspaces of the algebra of multiplication op...

In this paper, a new subspace method for predicting time-invariant/varying stochastic systems is investigated in the 4SID framework. Using the concept of angle between past and current subspaces spanned by the extended observability matrices, the future subspace is predicted by rotating current subspace in the geometrical sense. In order to treat even time-varying system, a recursive algorithm ...

Krylov subspace methods often exhibit superlinear convergence. We present a general analytic model which describes this superlinear convergence, when it occurs. We take an invariant subspace approach, so that our results apply also to inexact methods, and to non-diagonalizable matrices. Thus, we provide a unified treatment of the superlinear convergence of GMRES, Conjugate Gradients, block vers...