arXiv subjects
Publications and source records attributed to V. V. Fávaro.
We investigate the bounded composition operators induced by linear fractional self-maps of the right half-plane $\mathbb{C}_+$ on the Hardy space $H^2(\mathbb{C}_+).$ We completely characterize which of these operators are cohyponormal and we find conjugations for the linear fractional composition operators that are complex symmetric.
We investigate composition operators $C_Φ$ on the Hardy-Smirnov space $H^{2}(Ω)$ induced by analytic self-maps $Φ$ of an open simply connected proper subset $Ω$ of the complex plane. When the Riemann map $τ:\mathbb{U}\rightarrowΩ$ used to define the norm of $H^{2}(Ω)$ is a linear fractional transformation, we characterize the composition operators whose adjoints are composition operators. As applications of this fact, we provide a new proof for the adjoint formula discovered by Gallardo-Gutiérrez and Montes-Rodríguez and we give a new approach to describe all Hermitian and unitary composition operators on $H^{2}(Ω).$ Additionally, if the coefficients of $τ$ are real, we exhibit concrete examples of conjugations and describe the Hermitian and unitary composition operators which are complex symmetric with respect to specific conjugations on $H^{2}(Ω).$ We finish this paper showing that if $Ω$ is unbounded and $Φ$ is a non-automorphic self-map of $Ω$ with a fixed point, then $C_Φ$ is never complex symmetric on $H^{2}(Ω).$
We show that if $E$ is an arbitrary $(DFN)$-space, then every nontrivial convolution operator on the Fréchet nuclear space $\mathcal{H}(E)$ is mixing, in particular hypercyclic. More generally we obtain the same conclusion when $E=F^{\prime}_c,$ where $F$ is a separable Fréchet space with the approximation property. On the opposite direction we show that a translation operator on the space $\mathcal{H}(\mathbb{C}^{\mathbb{N}}) $ is never hypercyclic.
In this paper we continue the study initiated by Gurariy and Quarta in 2004 on the existence of linear spaces formed, up to the null vector, by continuous functions that attain the maximum only at one point. Inserting a topological flavor to the subject, we prove that results already known for functions defined on certain subsets of R are actually true for functions on quite general topological spaces. In the line of the original results of Gurariy and Quarta, we prove that, depending on the desired dimension, such subspaces may exist or not.
Let $(Ω,Σ,μ)$ be a measure space and $1< p < +\infty$. In this paper we show that, under quite general conditions, the set $L_{p}(Ω) - \bigcup\limits_{1 \leq q < p}L_{q}(Ω)$ is maximal spaceable, that is, it contains (except for the null vector) a closed subspace $F$ of $L_{p}(Ω)$ such that $\dim(F) = \dim(L_{p}(Ω))$. We also show that if those conditions are not fulfilled, then even the larger set $L_p(Ω) - L_q(Ω)$, $1 \leq q < p$, may fail to be maximal spaceable. The aim of the results presented here is, among others, to generalize all the previous work (since the 1960's) related to the linear structure of the sets $L_{p}(Ω) - L_{q}(Ω)$ with $q < p$ and $L_{p}(Ω) - \bigcup\limits_{1 \leq q < p}L_{q}(Ω)$.
In this short note we prove the result stated in the title; that is, for every $p>0$ there exists an infinite dimensional closed linear subspace of $L_{p}[0,1]$ every nonzero element of which does not belong to $\bigcup\limits_{q>p} L_{q}[0,1]$. This answers in the positive a question raised in 2010 by R. M. Aron on the spaceability of the above sets (for both, the Banach and quasi-Banach cases). We also complete some recent results from \cite{BDFP} for subsets of sequence spaces.
In this paper we use Nachbin's holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables.