In this paper, we study the structure of quasi-invariant subspaces of analytic Hilbert spaces over the complex plane. We especially investigate when two quasiinvariant subspaces are similar or unitarily equivalent for an analytic Hilbert space over the complex plane.  2002 Elsevier Science (USA)

Abstract. We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace [p] generated by a polynomial p with nonzero leading term, a quasi-invariant subspace M is similar to [p] if and only if there exists a polynomial q with the same leading term as p such that M = [q].

Abstract. In this paper some purely algebraic results are given concerning linear maps on algebras which preserve elements annihilated by a polynomial of degree greater than 1 and with no repeated roots and applied to linear maps on operator algebras such as standard operator algebras, von Neumann algebras and Banach algebras. Several results are obtained that characterize such linear maps in terms of homomorphisms, anti-homomorphisms, or, at least, Jordan homomorphisms.

In this note, we characterize maximal invariant subspaces for a class of operators. Let T be a Fredholm operator and 1−T T * ∈Sp for some p≥1. It is shown that if M is an invariant subspace for T such that dim M T M <∞, then every maximal invariant subspace of M is of codimension 1 in M . As an immediate consequence, we obtain that if M is a shift invariant subspace of the Bergman space and dim M zM <∞, then every maximal invariant subspace of M is of codimension 1 in M . We also apply the result to translation operators and their invariant subspaces.

No abstract