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Luis Rodríguez-Piazza

Publications and source records attributed to Luis Rodríguez-Piazza.

25 records · Page 2Linked to original sources
arXiv2018

Some examples of composition operators and their approximation numbers on the Hardy space of the bi-disk

We give examples of composition operators $C\_Φ$ on $H^2 (\D^2)$ showing that the condition $\|Φ\|\_\infty = 1$ is not sufficient for their approximation numbers $a\_n (C\_Φ)$ to satisfy $\lim\_{n \to \infty} [a\_n (C\_Φ) ]^{1/\sqrt{n}} = 1$, contrary to the $1$-dimensional case. We also give a situation where this implication holds. We make a link with the Monge-Ampère capacity of the image of $Φ$.

math.FA↗
arXiv2017

Approximation numbers of weighted composition operators

We study the approximation numbers of weighted composition operators $f\mapsto w\cdot(f\circφ)$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight $w$ can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples).

math.FA↗
arXiv2017

Absolutely summing Carleson embeddings on Hardy spaces

We consider the Carleson embeddings of the classical Hardy spaces (on the disk) into a L p ($μ$) space, where $μ$ is a Carleson measure on the unit disk. This includes the case of composition operators. We characterize such operators which are r-summing on H p , where p \textgreater{} 1 and r $\ge$ 1. This completely extends the former results on the subject and solves a problem open since the early seventies. Mathematics Subject Classification. Primary: 47B33 -- Secondary: 28A12; 30C85; 31A15; 46E20; 46E22; 47B06

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arXiv2016

Semigroups of composition operators and integral operators on mixed norm spaces

We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,α)$. First, we study the separable spaces $H(p,q,α)$ with $q<\infty,$ that behave as the Hardy and Bergman spaces. In the second part we deal with the spaces $H(p,\infty,α),$ where polynomials are not dense. To undertake this study, we introduce the integral operators, characterize its boundedness and compactness, and use its properties to find the maximal closed linear subspace of $H(p,\infty,α)$ in which the semigroups are strongly continuous. In particular, we obtain that this maximal space is either $H(p,0,α)$ or non-separable, being this result the deepest one in the paper.

math.FA↗
arXiv2013

Localizing algebras and invariant subspaces

It is shown that the algebra \(L^\infty(μ)\) of all bounded measurable functions with respect to a finite measure \(μ\) is localizing on the Hilbert space \(L^2(μ)\) if and only if the measure \(μ\) has an atom. Next, it is shown that the algebra \(H^\infty({\mathbb D})\) of all bounded analytic multipliers on the unit disc fails to be localizing, both on the Bergman space \(A^2({\mathbb D})\) and on the Hardy space \(H^2({\mathbb D}).\) Then, several conditions are provided for the algebra generated by a diagonal operator on a Hilbert space to be localizing. Finally, a theorem is provided about the existence of hyperinvariant subspaces for operators with a localizing subspace of extended eigenoperators. This theorem extends and unifies some previously known results of Scott Brown and Kim, Moore and Pearcy, and Lomonosov, Radjavi and Troitsky.

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