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Ideal structures in vector-valued polynomial spaces

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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


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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
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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