Bounded weak continuity of homogeneous polynomials at the origin

Christopher Boyd; R. A. Ryan

doi:10.1007/s000130050254

Bounded weak continuity of homogeneous polynomials at the origin

Christopher Boyd
, R. A. Ryan

Mathematics

University of Galway
University College Dublin

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

15 Citations (Scopus)

Abstract

Given a Banach space E we study P_w0(ⁿE), the space of all continuous n-homogeneous polynomials which are weakly continuous on bounded sets at the origin. We examine the coincidence of P_w0(ⁿE) with P(ⁿE), of P_w0(ⁿE) with P_w(ⁿE) and of P(ⁿE) with P_w(ⁿE) with particular interest as to when either of these coincidence for polynomials of degree n implies the corresponding coincidence for polynomials of lower degree.

Original language	English
Pages (from-to)	211-218
Number of pages	8
Journal	Archiv der Mathematik
Volume	71
Issue number	3
DOIs	https://doi.org/10.1007/s000130050254
Publication status	Published - 2 Sep 1998

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abstract = "Given a Banach space E we study Pw0(nE), the space of all continuous n-homogeneous polynomials which are weakly continuous on bounded sets at the origin. We examine the coincidence of Pw0(nE) with P(nE), of Pw0(nE) with Pw(nE) and of P(nE) with Pw(nE) with particular interest as to when either of these coincidence for polynomials of degree n implies the corresponding coincidence for polynomials of lower degree.",

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AU - Ryan, R. A.

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N2 - Given a Banach space E we study Pw0(nE), the space of all continuous n-homogeneous polynomials which are weakly continuous on bounded sets at the origin. We examine the coincidence of Pw0(nE) with P(nE), of Pw0(nE) with Pw(nE) and of P(nE) with Pw(nE) with particular interest as to when either of these coincidence for polynomials of degree n implies the corresponding coincidence for polynomials of lower degree.

AB - Given a Banach space E we study Pw0(nE), the space of all continuous n-homogeneous polynomials which are weakly continuous on bounded sets at the origin. We examine the coincidence of Pw0(nE) with P(nE), of Pw0(nE) with Pw(nE) and of P(nE) with Pw(nE) with particular interest as to when either of these coincidence for polynomials of degree n implies the corresponding coincidence for polynomials of lower degree.

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DO - 10.1007/s000130050254

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JF - Archiv der Mathematik

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Bounded weak continuity of homogeneous polynomials at the origin

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