Two Inner Sequences Based Invariant Subspaces in $${{H}^{2} (\mathbb{D}^{2})}$$ H 2 ( D 2 )

Abstract

Abstract. Let M be a shift invariant subspace in the vector-valued Hardy space H 2 E (D). The Beurling-Lax-Halmos theorem says that M can be completely characterized by Keywords.Hardy space over the bidisc, invariant subspace, operator-valued inner function, inner sequence, unitary equivalence, spectrum, core operator.

Inner multipliers and Rudin type invariant subspaces

“…The approach that we will take is inspired by the recent work of Y. Yang [17]. However, our results improve and generalize many results proved for the base case n = 2 in [17].…”

“…Here we present a similar result for Rudin type invariant subspaces in n-variables. The proof follows along the same lines as in Theorem 3.1 in [17]. Proof.…”

“…The unitary equivalence of inner sequence based invariant subspaces and two inner sequences based invariant subspaces of H 2 (D 2 ) are completely described in [11] and [17], respectively. Here we present a similar result for Rudin type invariant subspaces in n-variables.…”

Splitting Invariant Subspaces in the Hardy Space Over the Bidisk

“…We have K ϕ n (z) ⊗ K ψ n (w) ⊂ N for every −∞ < n < ∞. By (α3) and (α6) and by applying Lemma 3.5 we obtain the following corollary, which is proved by Yang [24,Theorem 4.3].…”

A Brief Survey of Operator Theory in H 2(𝔻2)

“…Due to its simple structure, innersequence-based submodule is useful for many purposes. We refer the readers to [82,103,105] for some of the applications.…”