Open Access
October 2016 Ideal structures in vector-valued polynomial spaces
Verónica Dimant, Silvia Lassalle, Ángeles Prieto
Banach J. Math. Anal. 10(4): 686-702 (October 2016). DOI: 10.1215/17358787-3649854


Note: An incorrect version of this article was posted from August 31, 2016, through September 7, 2016. The PDF is now correct.

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, Pw(nE,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(nE,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 Pw(nE,F) as an ideal in P(nE,F) to the range space F as an ideal in its bidual F.


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Verónica Dimant. Silvia Lassalle. Ángeles Prieto. "Ideal structures in vector-valued polynomial spaces." Banach J. Math. Anal. 10 (4) 686 - 702, October 2016.


Received: 3 December 2015; Accepted: 22 December 2015; Published: October 2016
First available in Project Euclid: 31 August 2016

zbMATH: 1352.46044
MathSciNet: MR3543907
Digital Object Identifier: 10.1215/17358787-3649854

Primary: 46G25
Secondary: 46B04 , 47H60‎ , 47L22

Keywords: HB-subspaces , homogeneous polynomials , weakly continuous on bounded sets polynomials

Rights: Copyright © 2016 Tusi Mathematical Research Group

Vol.10 • No. 4 • October 2016
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