Analytic norms in Orlicz spaces

Hájek, P.; Troyanski, S.

doi:10.1090/S0002-9939-00-05773-7

Analytic norms in Orlicz spaces
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Proc. Amer. Math. Soc. 129 (2001), 713-717 Request permission

Abstract:

It is shown that an Orlicz sequence space $h_M$ admits an equivalent analytic renorming if and only if it is either isomorphic to $l_{2n}$ or isomorphically polyhedral. As a consequence, we show that there exists a separable Banach space admitting an equivalent $C^\infty$-Fréchet norm, but no equivalent analytic norm.

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