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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

P-continuity on classical Banach spaces


Authors: P. Hájek and J. G. Llavona
Journal: Proc. Amer. Math. Soc. 128 (2000), 827-830
MSC (1991): Primary 46B03, 46B45
Published electronically: July 27, 1999
MathSciNet review: 1625749
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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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Additional Information

P. Hájek
Affiliation: Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain
Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: petr.hajek@math.tamu.edu, Department of Mathematics, Texas A&M University, College Station, Texas 77843

J. G. Llavona
Affiliation: Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain
Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: llavona@sunam1.mat.ucm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05056-X
PII: S 0002-9939(99)05056-X
Keywords: P-continuity
Received by editor(s): December 26, 1997
Received by editor(s) in revised form: April 29, 1998
Published electronically: July 27, 1999
Additional Notes: The first author’s research was supported by the Scholarship of The Ministry of Education and Science, Spain
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society