Banach Journal of Mathematical Analysis

Ideal structures in vector-valued polynomial spaces

Verónica Dimant, Silvia Lassalle, and Ángeles Prieto

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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.

Article information

Banach J. Math. Anal., Volume 10, Number 4 (2016), 686-702.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46G25: (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]
Secondary: 47H60: Multilinear and polynomial operators [See also 46G25] 46B04: Isometric theory of Banach spaces 47L22: Ideals of polynomials and of multilinear mappings

HB-subspaces homogeneous polynomials weakly continuous on bounded sets polynomials


Dimant, Verónica; Lassalle, Silvia; Prieto, Ángeles. Ideal structures in vector-valued polynomial spaces. Banach J. Math. Anal. 10 (2016), no. 4, 686--702. doi:10.1215/17358787-3649854.

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