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P-continuity on classical Banach spaces
Author(s):
P.
Hájek;
J.
G.
Llavona
Journal:
Proc. Amer. Math. Soc.
128
(2000),
827-830.
MSC (1991):
Primary 46B03, 46B45
Posted:
July 27, 1999
MathSciNet review:
1625749
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Abstract:
Given a Banach space  and an integer  , the existence of an  -homogeneous polynomial which is not uniformly continuous with respect to the polynomial topology on  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  (depending on  ).
References:
- [ACL]
- R. M. Aron, Y. S. Choi and J. G. Llavona, Estimates by Polynomials, Bull. Austral. Math. Soc. 52 (1995), 475-486. MR 96k:46073
- [D]
- J. Diestel, Sequences and series in Banach spaces, Grad. Texts in Math. 92, Springer, Berlin, 1984. MR 85i:46020
- [DJT]
- J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Univ. Press, 1996. MR 96i:46001
- [GGL]
- M. González, J. M. Gutiérrez and J. G. Llavona, Polynomial continuity on
 , Proc. Amer. Math. Soc. 125, no. 5 (1997), 1349-1353. MR 97g:46024 - [GL]
- J. M. Gutiérrez and J. G. Llavona, Polynomially continuous operators, Israel J. Math. 102 (1997), 179-183. MR 98k:46073
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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
Email:
llavona@sunam1.mat.ucm.es
DOI:
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
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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