Coherent sequences of polynomial ideals on Banach spaces

Carando, Daniel; Dimant, Verónica; Muro, Santiago

doi:10.1002/mana.200610791

Cited by 51 publications

(86 citation statements)

References 17 publications

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“…More general classes of analytic functions associated with coherent sequences of polynomial ideals were described in [8].…”

Section: Hilbert-schmidt Analyticitymentioning

confidence: 99%

Paley-Wiener Isomorphism Over Infinite-Dimensional Unitary Groups

Lopushansky

2017

Results Math

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Abstract. An analog of the Paley-Wiener isomorphism for the Hardy space with an invariant measure over infinite-dimensional unitary groups is described. This allows us to investigate on such space the shift and multiplicative groups, as well as, their generators and intertwining operators. We show applications to the Gauss-Weierstrass semigroups and to the Weyl-Schrödinger irreducible representations of complexified infinitedimensional Heisenberg groups.Mathematics Subject Classification. 46T12, 46G20.

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“…More general classes of analytic functions associated with coherent sequences of polynomial ideals were described in [8].…”

Section: Hilbert-schmidt Analyticitymentioning

confidence: 99%

Paley-Wiener Isomorphism Over Infinite-Dimensional Unitary Groups

Lopushansky

2017

Results Math

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“…Fortunately, in order to satisfy a multilinear Lindenstrauss theorem (in fact, in order to be stable), a much weaker property is sufficient. Coherent and multiplicative ideals of polynomials have been studied (also with different terminologies) in [19,16]. Here, we present a multilinear version of these properties (see [15], where similar properties for multilinear mappings are considered).…”

Section: Examples Of Multilinear Ideals Satisfying a Lindenstrauss Thmentioning

confidence: 99%

A Lindenstrauss theorem for some classes of multilinear mappings

Carando

Lassalle

Mazzitelli

2015

Journal of Mathematical Analysis and Applications

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Abstract. Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multlinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal all whose Arens extensions attain their norms at the same point. We prove a similar result for the class of symmetric multilinear mappings. We see that the quantitative (Bollobás-type) version of these results fails in every multilinear ideal.

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“…Carando, Dimant and Muro [9] (see also [7]) introduce the concept of coherent sequences of n-homogeneous Banach ideals of polynomials associated with Banach ideal of operators as follows. Given a Banach operator ideal A, the sequence (A n ) n of n-homogeneous polynomials is coherent and associated with A if there exist positive constants A and B such that for every Banach spaces X and Y the following conditions hold:…”

Section: By [19 Corollary 24] Lmentioning

confidence: 99%

$${\mathcal A}$$ A -compact mappings

Turco

2015

RACSAM

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Abstract. For a fixed Banach operator ideal A, we use the notion of A-compact sets of Carl and Stephani to study A-compact polynomials and A-compact holomorphic mappings. Namely, those mappings g : X → Y such that every x ∈ X has a neighborhood V x such that g(V x ) is relatively A-compact. We show that the behavior of A-compact polynomials is determined by its behavior in any neighborhood of any point. We transfer some known properties of A-compact operators to A-compact polynomials. In order to study A-compact holomorphic functions, we appeal to the A-compact radius of convergence which allows us to characterize the functions in this class. Under certain hypothesis on the ideal A, we give examples showing that our characterization is sharp.

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Coherent sequences of polynomial ideals on Banach spaces

Cited by 51 publications

References 17 publications

Paley-Wiener Isomorphism Over Infinite-Dimensional Unitary Groups

Paley-Wiener Isomorphism Over Infinite-Dimensional Unitary Groups

A Lindenstrauss theorem for some classes of multilinear mappings

$${\mathcal A}$$ A -compact mappings

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