Hypercyclicity, existence and approximation results for convolution operators on spaces of entire functions

A standard technique in infinite dimensional holomorphy, which produced several useful results, uses the Borel transform to represent linear functionals on certain spaces of multilinear operators between Banach spaces as multilinear operators. In this paper, we develop a technique to represent linear functionals, as linear operators, on spaces of multilinear operators that are beyond the scope of the standard technique. Concrete applications to some well-studied classes of multilinear operators, including the class of compact multilinear operators, and to one new class are provided. We can see, in particular, that sometimes our representations hold under conditions less restrictive than those of the related classical ones.

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“…Recent developments, including applications to linear dynamics, can be found, e.g., in Refs. [2,7,[15][16][17][18]27].…”

Section: Introductionmentioning

confidence: 99%

On the representation of linear functionals on hyper-ideals of multilinear operators

Botelho

Wood

2020

Banach J. Math. Anal.

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“…The books [12,13] by Dineen are excellent sources for results of this kind and their many applications. Recent developments, including applications to linear dynamics, can be found, e.g., in [2,7,15,16,17,18,27].…”

Section: Introductionmentioning

confidence: 99%

On the representation of linear functionals on hyper-ideals of multilinear operators

Botelho¹,

Wood²

2020

Preprint

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A standard technique in infinite dimensional holomorphy, which produced several useful results, uses the Borel transform to represent linear functionals on certain spaces of multilinear operators between Banach spaces as multilinear operators. In this paper we develop a technique to represent linear functionals, as linear operators, on spaces of multilinear operators that are beyond the scope of the standard technique. Concrete applications to some well studied classes of multilinear operators, including the class of compact multilinear operators, and to one new class are provided. We can see, in particular, that sometimes our representations hold under conditions less restrictive than those of the related classical ones.

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“…Isso foi feito muitas vezes na literatura, e muitas aplicações dessa técnica foram obtidas, incluindo aplicações na área de dinâmica linear (veja [15,25,35,36,38,39,40,41,58]). Destacaremos três exemplos de aplicações da transformada de Borel que nos serão úteis mais adiante.…”

Section: Capítulo 3 Representação De Duaisunclassified

“…onde Q( n E; F ) é um subespaço de P( n E; F ) munido de uma norma completa • Q e contendo os polinômios de tipo finito. Muitas aplicações dessa transformada podem ser encontradas na literatura, por exemplo [4,25,31,35,37,38,39,40,41,47,52,58].…”

Section: A Hiper-transformada De Borel Polinomialunclassified

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Representação de funcionais lineares em hiper-ideais de operadores multilineares e de polinômios homogêneos

Noronha¹

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Nesta tese introduzimos a hiper-transformada de Borel como ferramenta para representar funcionais lineares em hiper-ideais de operadores multilineares entre espaços de Banach. E também a hiper-transformada de Borel polinomial para representar funcionais lineares em hiper-ideais de polinômios homogêneos. Essas transformadas são aplicadas para representar funcionais lineares em espaços de operadores multilineares e polinômios homogêneos que são: aproximáveis por operadores/polinômios de posto finito, compactos, hiper-(s; r)-nucleares e hiper-σ(p)-nucleares. Uma nova técnica para gerar hiper-ideais de operadores multilineares e hiper-ideais e ideais bilaterais de polinômios também é desenvolvida.Palavras-chave: Espaços de Banach, hiper-ideais, representação de funcionais lineares, operadores multilineares, hiper-transformada de Borel, polinômios homogêneos, hipertransformada de Borel polinomial.

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Hypercyclicity, existence and approximation results for convolution operators on spaces of entire functions

Cited by 4 publications

References 44 publications

On the representation of linear functionals on hyper-ideals of multilinear operators

On the representation of linear functionals on hyper-ideals of multilinear operators

On the representation of linear functionals on hyper-ideals of multilinear operators

Representação de funcionais lineares em hiper-ideais de operadores multilineares e de polinômios homogêneos

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