Synnatzschke’s theorem for polynomials

Christopher Boyd; Raymond A. Ryan; Nina Snigireva

doi:10.1007/s11117-020-00760-y

Synnatzschke’s theorem for polynomials

Christopher Boyd
, Raymond A. Ryan
, Nina Snigireva

Mathematics

University College Dublin

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

Abstract

We establish a multilinear generalisation of Synnatzschke’s Theorem for regular operators on Banach lattices, with the Arens adjoint taking the place of the transpose. Using this result, we show that the Aron–Berner extension of a regular homogeneous polynomial to the order continuous bidual preserves the absolute value. As a consequence, it follows that the regular norm is preserved by the Aron–Berner extension.

Original language	English
Pages (from-to)	229-242
Number of pages	14
Journal	Positivity
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s11117-020-00760-y
Publication status	Published - Feb 2021

Keywords

Banach lattice
Order-continuous bidual
Polynomial
Synnatzschke’s theorem

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10.1007/s11117-020-00760-y

Cite this

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abstract = "We establish a multilinear generalisation of Synnatzschke{\textquoteright}s Theorem for regular operators on Banach lattices, with the Arens adjoint taking the place of the transpose. Using this result, we show that the Aron–Berner extension of a regular homogeneous polynomial to the order continuous bidual preserves the absolute value. As a consequence, it follows that the regular norm is preserved by the Aron–Berner extension.",

keywords = "Banach lattice, Order-continuous bidual, Polynomial, Synnatzschke{\textquoteright}s theorem",

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AU - Ryan, Raymond A.

AU - Snigireva, Nina

PY - 2021/2

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N2 - We establish a multilinear generalisation of Synnatzschke’s Theorem for regular operators on Banach lattices, with the Arens adjoint taking the place of the transpose. Using this result, we show that the Aron–Berner extension of a regular homogeneous polynomial to the order continuous bidual preserves the absolute value. As a consequence, it follows that the regular norm is preserved by the Aron–Berner extension.

AB - We establish a multilinear generalisation of Synnatzschke’s Theorem for regular operators on Banach lattices, with the Arens adjoint taking the place of the transpose. Using this result, we show that the Aron–Berner extension of a regular homogeneous polynomial to the order continuous bidual preserves the absolute value. As a consequence, it follows that the regular norm is preserved by the Aron–Berner extension.

KW - Banach lattice

KW - Order-continuous bidual

KW - Polynomial

KW - Synnatzschke’s theorem

UR - https://www.scopus.com/pages/publications/85084424033

U2 - 10.1007/s11117-020-00760-y

DO - 10.1007/s11117-020-00760-y

M3 - Article

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VL - 25

SP - 229

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JO - Positivity

JF - Positivity

IS - 1

ER -

Synnatzschke’s theorem for polynomials

Abstract

Keywords

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