Duality in Spaces of Nuclear and Integral Polynomials

Carando, Daniel; Dimant, Verónica

doi:10.1006/jmaa.1999.6626

Cited by 33 publications

(33 citation statements)

References 12 publications

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“…Recall that polynomials that are weakly continuous on bounded sets are precisely those which are K-bounded, for some compact subset K of E ~ (see [24] and [4] for the scalar-valued case, and [8] for the vector-valued case). For any bounded set K, the Aron Berner extension of an X-valued K-bounded polynomial is an X ~-valued K-bounded polynomial (see [6]).…”

Section: Lemma 21 Let Aels(ne;x) Ifta:e-+l~( ~ 1e;x) Is a Weakly Cmentioning

confidence: 99%

E′ and its relation with vector-valued functions on E

Carando¹,

Lassalle²

2004

Ark. Mat.

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Abstract. We study the relation between different spaces of vector-valued polynomials and analytic functions over dual-isomorphic Banach spaces. Under conditions of regularity on E and F, we show that the spaces of X-vahed n-homogeneous polynomials and analytic functions of bounded type on E and F are isomorphic whenever X is a dual space. Also, we prove that many of the usual subspaces of polynomials and analytic functions on E and F are isomorphic without conditions on the involved spaces.

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Section: Lemma 21 Let Aels(ne;x) Ifta:e-+l~( ~ 1e;x) Is a Weakly Cmentioning

confidence: 99%

E′ and its relation with vector-valued functions on E

Carando¹,

Lassalle²

2004

Ark. Mat.

Self Cite

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“…It therefore follows from [6, Proposition 3] (see also [8,Theorem 1.5]) that P I ( n E) is isometrically isomorphic to P N ( n E). As E has the approximation property it follows that P( n E ) is the bidual of n,s, E. Further, as the norm on E is Fréchet differentiable, it follows from [6,Corollary 15] that the set of strongly exposed points of the unit ball of P I ( n E) is equal to the set {±ϕ n : ϕ ∈ E , ϕ = 1}.…”

Section: Theorem 17mentioning

confidence: 99%

Centralisers of spaces of symmetric tensor products and applications

Boyd

Lassalle

2006

Math. Z.

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We show that the centraliser of the space of n-fold symmetric injective tensors, n ≥ 2, on a real Banach space is trivial. With a geometric condition on the set of extreme points of its dual, the space of integral polynomials we obtain the same result for complex Banach spaces. We give some applications of this results to centralisers of spaces of homogeneous polynomials and complex Banach spaces. In addition, we derive a Banach-Stone Theorem for spaces of vector-valued approximable polynomials.

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“…By use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1446788700008946 [5] Nuclear and integral polynomials 273 <g>™£ := E<g> s W ® S E we denote the w-fold symmetric tensor product of E, that is, the set of all elements u e ® m £ of the form n u = ^ A.;*;® W ®xj (n e N, A. , -e K,xj e £, 1 < j < n).…”

Section: < C Supmentioning

confidence: 99%