Nuclear and integral polynomials

Cilia, Raffaella; Gutiérrez, Joaquín M.

doi:10.1017/s1446788700008946

Cited by 10 publications

(4 citation statements)

References 13 publications

(25 reference statements)

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“…In [11,Theorem 3], the authors show that whenever E has the approximation property and the Radon-Nikodým property, the spaces of Grothendieck integral and nuclear n-homogeneous polynomials from E to any Banach space are isomorphic. Proposition 1 allows us to show that the isomorphism is in fact an isometry.…”

Section: Definitions and General Resultsmentioning

confidence: 99%

Extension of vector-valued integral polynomials

Carando

Lassalle

2005

Journal of Mathematical Analysis and Applications

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We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they are extendible to X-valued polynomials. The Aron-Berner extension of an integral polynomial is also studied. A canonical integral representation is given for domains not containing 1 .

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Section: Definitions and General Resultsmentioning

confidence: 99%

Extension of vector-valued integral polynomials

Carando

Lassalle

2005

Journal of Mathematical Analysis and Applications

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“…Nuclear polynomials between Banach spaces have been studied by many authors; see [2], [3], [4] and [15].…”

Section: Algebras Of Polynomials Generated By Linear Operatorsmentioning

confidence: 99%

Algebras of Polynomials Generated by Linear Operators

Zaj¹,

Abtahi²

2023

Preprint

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) is an A-valued uniform algebra and that, under certain conditions, it is isometrically isomorphic to the injective tensor product P N (K) ⊗ǫ A, where P N (K) is the uniform algebra on K generated by nuclear scalar-valued polynomials. The character space of È(K, A) is then identified with KN × M(A), where KN is the nuclear polynomially convex hull of K in E, and M(A) is the character space of A.

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“…The factorisations of the next theorem are proved in [13,Proposition 6]. Here we add the equalities of the norms.…”

Section: Relationship With Other Ideals Of Polynomialsmentioning

confidence: 99%

“…Using the left integral 1 -factorisation property, we can improve the results of [13,Proposition 5]. …”

Section: Theorem 35 Consider the Operators T ∈ L(e F) And S ∈ L(fmentioning

confidence: 99%

LEFT ℓ₁-FACTORABLE POLYNOMIALS

Cilia¹,

Gutiérrez²

2009

Glasgow Math. J.

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We characterise the Radon-Nikodým property by the left 1 -factorisation of polynomials on L 1 (μ). We study the left 1 -factorisation of nuclear, compact and Pietsch integral polynomials. For Pietsch integral polynomials, we introduce the left integral 1 -factorisation property, obtaining a second polynomial characterisation of the Radon-Nikodým property and showing that it plays a role somehow comparable, in this setting, to nuclearity of operators. A characterisation of L 1 -spaces is also given in terms of the left compact 1 -factorisation of polynomials.2000 Mathematics Subject Classification. Primary 46G25; secondary 47H60, 46B20, 46B22.

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Nuclear and integral polynomials

Cited by 10 publications

References 13 publications

Extension of vector-valued integral polynomials

Extension of vector-valued integral polynomials

Algebras of Polynomials Generated by Linear Operators

LEFT ℓ₁-FACTORABLE POLYNOMIALS

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Nuclear and integral polynomials

Cited by 10 publications

References 13 publications

Extension of vector-valued integral polynomials

Extension of vector-valued integral polynomials

Algebras of Polynomials Generated by Linear Operators

LEFT ℓ1-FACTORABLE POLYNOMIALS

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Product

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LEFT ℓ₁-FACTORABLE POLYNOMIALS