Related papers: Reducing Subspaces of de Branges-Rovnyak Spaces

Let $L= -\Delta_{\mathbb{H}^n}+V$ be a Schr\"odinger operator on the Heisenberg group $\mathbb{H}^n$, where $\Delta_{\mathbb{H}^n}$ is the sub-Laplacian and the nonnegative potential $V$ belongs to the reverse H\"older class…

This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are…

Consider a Hilbert space obtained as the completion of the polynomials C[z} in m-variables for which the mnonomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same…

A d-contraction is a d-tuple $(T_1,...,T_d)$ of mutually commuting operators acting on a common Hilbert space H such that $ \|T_1\xi_1+T_2\xi_2+... +T_d\xi_d\|^2\leq \|\xi_1\|^2+\|\xi_2\|^2+...+\|\xi_d\|^2 $ for all…

Motivated by the canonical decomposition of contractions on Hilbert spaces, we investigate when contractive Toeplitz operators on vector-valued Hardy spaces on the unit disc admit a non-zero reducing subspace on which its restriction is…

We study a general metric constrained interpolation problem in a de Branges-Rovnyak space $\mathcal{H}(K_S)$ associated with a contractive multiplier $S$ between two Fock spaces along with its commutative counterpart, a de Branges-Rovnyak…

Given a holomorphic self-map $\varphi$ of $\D$ (the open unit disc in $\mathbb{C}$), the composition operator $C_{\varphi} f = f \circ \varphi$, $f \in H^2(\mathbb{\D})$, defines a bounded linear operator on the Hardy space…

A bounded linear Hilbert space operator $S$ is said to be a $2$-isometry if the operator $S$ and its adjoint $S^*$ satisfy the relation $S^{*2}S^{2} - 2 S^{*}S + I = 0$. In this paper, we study Hilbert space operators having liftings or…

In this paper, the analysis of nearly invariant subspaces and kernels of Toeplitz operators on the Hardy space over the bidisk is developed. Firstly, we transcribe Chalendar, Chevrot and Partington's result to vector-valued Hardy space…

We study the behaviour on rearrangement-invariant spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fractional version), the Hilbert and Stieltjes transforms, and the…

We study the problem of characterizing the cyclic vectors in de Branges-Rovnyak spaces. Based on a description of the invariant subspaces we show that the difficulty lies entirely in understanding the subspace $(aH^{2})^{\perp}$ and give a…

In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…

It is proved that a commutative algebra $A$ of operators on a reflexive real Banach space has an invariant subspace if each operator $T\in A$ satisfies the condition $$\|1- \varepsilon T^2\|_e \le 1 + o(\varepsilon) \text{ when }…

For $1/2<p<1$, a description of inner functions whose derivative is in the Hardy space $H^p$ is given in terms of either their mapping properties or the geometric distribution of their zeros.

In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces $\mathcal{H}(b)$, mainly when b is a non-extreme point of the unit ball of $H^{\infty}$.

Let $L=-\Delta+V$ be a Schr\"odinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this article, we will introduce weighted Hardy spaces $H^p_L(w)$…

We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $\Lambda^p_u(w)$. We start by giving several necessary conditions that, in particular, lead us to the complete…

Two problems are posed that involve the star-invariant subspace $K^p_\theta$ (in the Hardy space $H^p$) associated with an inner function $\theta$. One of these asks for a characterization of the extreme points of the unit ball in…

It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…

We prove that functions continuous up to the boundary are dense in de Branges-Rovnyak spaces induced by extreme points the unit ball of $H^\infty$.