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Analytic norms in Orlicz spaces


Authors: P. Hájek and S. Troyanski
Journal: Proc. Amer. Math. Soc. 129 (2001), 713-717
MSC (2000): Primary 46B03, 46B45
DOI: https://doi.org/10.1090/S0002-9939-00-05773-7
Published electronically: November 8, 2000
MathSciNet review: 1801996
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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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Additional Information

P. Hájek
Affiliation: Departamento Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain and Mathematical Institute, Czech Academy of Science, Žitná 25, Prague, Czech Republic
Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: phajek@math.tamu.edu

S. Troyanski
Affiliation: Departmento Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain and Department of Mathematics and Informatics, Sofia University, 5, James Bourchier Blvd., 1126 Sofia, Bulgaria

DOI: https://doi.org/10.1090/S0002-9939-00-05773-7
Keywords: Analytic norm, Orlicz space, polyhedral space
Received by editor(s): March 30, 1998
Received by editor(s) in revised form: November 25, 1998
Published electronically: November 8, 2000
Additional Notes: The second author was partially supported by NFSR of Bulgaria, Grant MM-808-98
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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