Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 4 (2016), 686-702.
Ideal structures in vector-valued polynomial spaces
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 and Banach spaces, whether the class of -homogeneous polynomials, , which are weakly continuous on bounded sets, is an HB-subspace or an -ideal in the space of continuous -homogeneous polynomials, . 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 as an ideal in to the range space as an ideal in its bidual .
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
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.bjma/1472657852