Synnatzschkes Theorem for Polynomials

Raymond A. Ryan

Synnatzschkes Theorem for Polynomials

Raymond A. Ryan

Mathematics

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Abstract

We establish a multilinear generalization of Synnatzschkes 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 (Ireland)
Journal	Positivity
Publication status	Published - 1 Jan 2020

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Christopher Boyd, Raymond A.Ryan & Nina Snigireva

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title = "Synnatzschkes Theorem for Polynomials",

abstract = "We establish a multilinear generalization of Synnatzschkes 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.",

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T1 - Synnatzschkes Theorem for Polynomials

AU - Ryan, Raymond A.

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N2 - We establish a multilinear generalization of Synnatzschkes 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 generalization of Synnatzschkes 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.

M3 - Article

JO - Positivity

JF - Positivity

ER -

Synnatzschkes Theorem for Polynomials

Abstract

Authors (Note for portal: view the doc link for the full list of authors)

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Cite this