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Dimant, Verónica and Lassalle, Silvia and Prieto Yerro, M. Ángeles
(2016)
*Ideal structures in vector-valued polynomial spaces.*
Banach Journal of Mathematical Analysis, 10
(4).
pp. 686-702.
ISSN 1735-8787

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Official URL: https://projecteuclid.org/euclid.bjma/1472657852

## Abstract

This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of n-homogeneous polynomials, 'P-w((n) E, F), which are weakly continuous on bounded sets, is an HB-subspace or an M(1, C)-ideal in the space of continuous n-homogeneous polynomials, P((n) E, F). We establish sufficient conditions under which the problem can be positively solved. Some examples are given. We also study when some ideal structures pass from P-w((n) E, F) as an ideal in P((n) E, F) to the range space F as an ideal in its bidual F**.

Item Type: | Article |
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Uncontrolled Keywords: | HB-subspaces; Homogeneous polynomials; Weakly continuous on bounded sets polynomials |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 40735 |

Deposited On: | 02 Feb 2017 10:04 |

Last Modified: | 02 Feb 2017 11:13 |

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