Ideals of polynomials between Banach spaces revisited

Velanga, T.

doi:10.1080/03081087.2017.1394963

Cited by 14 publications

(10 citation statements)

References 16 publications

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“…Special types of multi-ideals and of polynomial ideals were introduced and developed in [10,12,13,14,23,32,38] taking into account the composition with multilinear operators/homogeneous polynomials instead of only with linear operators. More precisely:…”

Section: Introductionmentioning

confidence: 99%

Hyper-ideals of multilinear operators and two-sided polynomial ideals generated by sequence classes

Botelho¹,

Wood²

2021

Preprint

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Section: Introductionmentioning

confidence: 99%

Hyper-ideals of multilinear operators and two-sided polynomial ideals generated by sequence classes

Botelho¹,

Wood²

2021

Preprint

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“…Hyper-ideals of multilinear operators, in the sense of Refs. [6,32], contain the finite-rank operators, and this is the reason why we shall apply the hyper-Borel transform to represent functionals on hyper-ideals.…”

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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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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“…If n 1 = · · · = n m = n we use P a ( n, m ...,n E; F ) instead. The concept of multipolynomials was firstly discovered by I. Chernega and A. Zagorodnyuk in [3] and was rediscovered in [13], in the current notation/language, intending to present a unified multilinear/polynomial theory which had been following in apparently disjoint lines of research (see [2,13]).…”

Section: Introductionmentioning

confidence: 99%

Multilinear mappings versus homogeneous polynomials and a multipolynomial polarization formula

Velanga

2019

Linear and Multilinear Algebra

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We show that (k, m)-linear mappings, introduced by I. Chernega and A. Zagorodnyuk in [3], are particular cases of polynomials. As corollaries, we expose some apparently overlooked properties in the literature. For instance, every multilinear mapping is a homogeneous polynomial. Contributions to the polarization formula are also provided.2010 Mathematics Subject Classification. Primary 46G20, 46G25, 47H60; Secondary 15A99 .

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Ideals of polynomials between Banach spaces revisited

Cited by 14 publications

References 16 publications

Hyper-ideals of multilinear operators and two-sided polynomial ideals generated by sequence classes

Hyper-ideals of multilinear operators and two-sided polynomial ideals generated by sequence classes

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

Multilinear mappings versus homogeneous polynomials and a multipolynomial polarization formula

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