Ideal structures in vector-valued polynomial spaces

DIMANT, V. ; LASSALLE, S.; PRIETO, A.

BANACH JOURNAL OF MATHEMATICAL ANALYSIS

BANACH MATHEMATICAL RESEARCH GROUP

Año: 2016 vol. 10 p. 686 - 702

1735-8787

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