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A multilinear Phelps' Lemma
Author(s):
Richard
Aron;
Antonia
Cardwell;
Domingo
García;
Ignacio
Zalduendo
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2549-2554.
MSC (2000):
Primary 46B20;
Secondary 47A07
Posted:
February 6, 2007
MathSciNet review:
2302575
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Abstract:
We prove a multilinear version of Phelps' Lemma: if the zero sets of multilinear forms of norm one are `close', then so are the multilinear forms.
References:
-
- 1.
- Acosta, M., Aguirre, F., and Payá, R. There is no bilinear Bishop-Phelps Theorem. Israel J. of Math. 93 (1996), 221-228. MR 1380644 (97d:46018)
- 2.
- Aron, R., Downey, L., and Maestre, M. Zero sets and linear dependence of multilinear forms. Note di Mat., (1) 25, 2005-2006 (2006), 49-54. MR 2220451
- 3.
- Bishop, E. and Phelps, R. A proof that every Banach space is subreflexive. Bull. Amer. Math. Soc., 67 (1961), 97-98. MR 0123174 (23:A503)
- 4.
- Benítez, C., Sarantopoulos, Y., and Tonge, A. Lower bounds for the norms of products of polynomials. Math. Proc. Cambridge Philos. Soc., 124 (1998), 395-408. MR 1636556 (99h:46077)
- 5.
- Cardwell, A. A new proof of a Lemma by Phelps, International Journal of Mathematics and Mathematical Sciences, Vol. 2006 (2006).
- 6.
- Fabian, M., Habala, P., Hájek, P., Montesinos, V., Pelant, P., and Zizler, V. Functional Analysis and Infinite-Dimensional Geometry. CMS Books in Mathematics. Springer-Verlag, 2001. MR 1831176 (2002f:46001)
- 7.
- Fabian, M., Montesinos, V., and Zizler, V. A characterization of subspaces of weakly compactly generated Banach spaces. J. London Math. Soc. (2) 69 (2004), 457-464. MR 2040615 (2004k:46026)
- 8.
- Phelps, R. A representation theorem for bounded convex sets. Proc. Amer. Math. Soc., 11 (1960), 976-983. MR 0123172 (23:A501)
- 9.
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Additional Information:
Richard
Aron
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email:
aron@math.kent.edu
Antonia
Cardwell
Affiliation:
Mathematics Department, Millersville University, P.O. Box 1002, Millersville, Pennsylvania 17551-0302
Email:
Antonia.Cardwell@millersville.edu
Domingo
García
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain
Email:
domingo.garcia@uv.es
Ignacio
Zalduendo
Affiliation:
Depto. de Matemática, Universidad Torcuato Di Tella, Miñones 2159/77 (C1428ATG), Buenos Aires, Argentina
Email:
nacho@utdt.edu
DOI:
10.1090/S0002-9939-07-08762-X
PII:
S 0002-9939(07)08762-X
Keywords:
Phelps' Lemma,
multilinear forms
Received by editor(s):
February 9, 2006
Received by editor(s) in revised form:
April 11, 2006
Posted:
February 6, 2007
Additional Notes:
The first and third authors were partially supported by MEC and FEDER Project MTM2005-08210.
The fourth author was supported by a Fulbright Commission grant
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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