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Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces

M. Jimenéz Sevilla, Rafael Payá (1998)

Studia Mathematica

For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space of all continuous N-linear forms on X, but there are continuous (N+1)-linear forms on X which cannot be approximated by norm attaining (N+1)-linear forms. Actually,X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.

Normed barrelled spaces

Christopher Stuart (2000)

Banach Center Publications

In this paper we present a general “gliding hump” condition that implies the barrelledness of a normed vector space. Several examples of subspaces of l 1 are shown to be barrelled using the theorem. The barrelledness of the space of Pettis integrable functions is also implied by the theorem (this was first shown in [3]).

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