𝑃-continuity on classical Banach spaces

Hájek, P.; Llavona, J.

doi:10.1090/S0002-9939-99-05056-X

$\text {P}$-continuity on classical Banach spaces
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by P. Hájek and J. G. Llavona PDF

Proc. Amer. Math. Soc. 128 (2000), 827-830 Request permission

Abstract:

Given a Banach space $X$ and an integer $n$, the existence of an $n$- homogeneous polynomial which is not uniformly continuous with respect to the polynomial topology on $B_X$ is investigated. We provide a complete characterization for some classical Banach spaces, while for others a surprising unresolved difficulty is encountered for a certain value of $n$ (depending on $X$).

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