Extendibility of homogeneous polynomials on Banach spaces

Pádraig Kirwan; Raymond A. Ryan

doi:10.1090/s0002-9939-98-04009-x

Extendibility of homogeneous polynomials on Banach spaces

Pádraig Kirwan
, Raymond A. Ryan

Mathematics

University of Galway

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

29 Citations (Scopus)

Abstract

We study the n-homogeneous polynomials on a Danach space X that can be extended to any space containing X. We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible n-homogeneous polynomials on X and we characterize the extendible 2-homogeneous polynomials on X when X is a Hilbert space, an L₁-space or an L_∞-space.

Original language	English
Pages (from-to)	1023-1029
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	126
Issue number	4
DOIs	https://doi.org/10.1090/s0002-9939-98-04009-x
Publication status	Published - 1998

Keywords

Extendibility
Homogeneous polynomial

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10.1090/s0002-9939-98-04009-x

Cite this

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AB - We study the n-homogeneous polynomials on a Danach space X that can be extended to any space containing X. We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible n-homogeneous polynomials on X and we characterize the extendible 2-homogeneous polynomials on X when X is a Hilbert space, an L1-space or an L∞-space.

KW - Extendibility

KW - Homogeneous polynomial

UR - https://www.scopus.com/pages/publications/22044439741

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DO - 10.1090/s0002-9939-98-04009-x

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Extendibility of homogeneous polynomials on Banach spaces

Abstract

Keywords

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