arXiv subjects

Daniel Suárez

Publications and source records attributed to Daniel Suárez.

8 recordsLinked to original sources

arXiv2023

Frames of iterations and vector-valued model spaces

Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0 and I = Z. The characterization for unilateral iterations gives a similarity with the compression of the shift acting on model spaces of the Hardy space of analytic functions defined on the unit disk with values in $l^2(J). This generalizes recent work for iterations of a single function. In the case of bilateral iterations, the characterization is by the bilateral shift acting on doubly invariant subspaces of L^2(T,l^2(J)). Furthermore, we characterize the frames of iterations for vector-valued model operators when J is finite in terms of Toeplitz and multiplication operators in the unilateral and bilateral case, respectively. Finally, we study the problem of finding the minimal number of orbits that produce a frame in this context.

math.FA↗

arXiv2022

On the analytic structure of the $H^\infty$ maximal ideal space

We characterize the algebra $H^\infty \circ L_{m}$, where $m$ is a point of the maximal ideal space of $H^\infty$ with nontrivial Gleason part $P(m)$ and $L_{m} : \mathbb{D}\to P(m)$ is the coordinate Hoffman map. In particular, it is shown that for any continuous function $f: P(m) \to \mathbb{C}$ with $f\circ L_{m} \in H^\infty$ there exists $F\in H^\infty$ such that $F|_{P(m)} = f$.

math.FA↗

arXiv2020

Multi-orbital frames through model spaces

We characterize the normal operators $A$ on $\ell^2$ and the elements $a^i \in \ell^2$, with $1\le i\le m$, such that the sequence $$\{ A^n a^1 , \ldots , A^n a^m \}_{n\ge 0}$$ is a frame. The characterization makes strong use of the pseudo-hyperbolic metric of $\mathbb{D}$ and is given in terms of the backward shift invariant subspaces of $H^2(\mathbb{D})$ associated to finite products of interpolating Blaschke products.

math.FA↗

arXiv2013

A generalization of Toeplitz operators on the Bergman space

If $μ$ is a finite measure on the unit disc and $k\ge 0$ is an integer, we study a generalization derived from Englis's work, $T_μ^{(k)}$, of the traditional Toeplitz operators on the Bergman space $A^2$, which are the case $k=0$. Among other things, we prove that when $μ\ge 0$, these operators are bounded if and only if $μ$ is a Carleson measure, and we obtain some estimates for their norms.

math.FA↗

arXiv2012

The Essential Norm of Operators on $A^p_α(\mathbb{B}_n)$

In this paper we characterize the compact operators on $A^p_α(\mathbb{B}_n)$ when $1 -1$. The main result shows that an operator on $A^p_α(\mathbb{B}_n)$ is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.

math.CA↗

arXiv2011

Orbits of non-elliptic disc automorphisms

Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace $H^2$ generated by the limit points in the $H^2$ norm of the orbit of a thin Blaschke product $B$ under composition operators $C_ϕ$ induced by non-elliptic automorphisms. This description exhibits a surprising connection to model spaces. Finally, we give a constructive characterization of the $C_ϕ$-eigenfunctions in $H^p$ for $1\le p\le \infty$.

math.FA↗

arXiv2010

Paths of inner-related functions

We characterize the connected components of the subset $\cni$ of $H^\infty$ formed by the products $bh$, where $b$ is Carleson-Newman Blaschke product and $h\in H^\infty$ is an invertible function. We use this result to show that, except for finite Blaschke products, no inner function in the little Bloch space is in the closure of one of these components. Our main result says that every inner function can be connected with an element of $\cni$ within the set of products $uh$, where $u$ is inner and $h$ is invertible. We also study some of these issues in the context of Douglas algebras.

math.CA↗

arXiv2007

The eigenvalues of limits of radial Toeplitz operators

Let $A^2$ be the Bergman space on the unit disk. A bounded operator $S$ on $A^2$ is called radial if $Sz^n = λ_n z^n$ for all $n\ge 0$, where $λ_n$ is a bounded sequence of complex numbers. We characterize the eigenvalues of radial operators that can be approximated by Toeplitz operators with bounded symbols.

math.FA↗