Proceedings of the American Mathematical Society

Author(s): Daniel Carando; Verónica Dimant
Journal: Proc. Amer. Math. Soc. 135 (2007), 1769-1773.
MSC (2000): Primary 46G25, 46B28
Posted: November 7, 2006
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Abstract: We show that for every infinite-dimensional normed space

and every $k\geq 3$ there are extendible

-homogeneous polynomials which are not integral. As a consequence, we prove a symmetric version of a result of John.

1.: Ansemil, José and Floret, Klaus. The symmetric tensor product of a direct sum of locally convex spaces, Studia Math. 129 (1998), 285-295. MR 1609655 (99b:46003)
2.: Boas, Harold P. Majorant series, J. Korean Math. Soc. 37 (2000), no. 2, 321-337. MR 1775963 (2001j:32001)
3.: Carando, Daniel. Extendible polynomials on Banach spaces, J. Math. Anal. Appl. 233 (1999), no. 1, 359-372. MR 1684392 (2000d:46057)
4.: -, Extendibility of polynomials and analytic functions on $\ell_p$ , Studia Math. 145 (2001), no. 1, 63-73.MR 1828993 (2002d:46042)
5.: Carando, Daniel; Dimant, Verónica and Sevilla-Peris, Pablo. Limit orders and multilinear forms on $\ell_p$ spaces, Publ. Res. Inst. Math. Sci., 42, no. 2, (2006), 507-522.
6.: Castillo, Jesús M. F.; García, Ricardo and Jaramillo, Jesús A. Extension of bilinear forms on Banach spaces, Proc. Amer. Math. Soc. 129 (2001), no. 12, 3647-3656. MR 1860499 (2002i:46017)
7.: Defant, Andreas and Floret, Klaus. Tensor norms and operator ideals. North-Holland, Amsterdam, 1993. MR 1209438 (94e:46130)
8.: Díaz, Juan Carlos and Dineen, Seán. Polynomials on stable spaces, Ark. Mat. 36 (1998), 87-96. MR 1611149 (99a:46082)
9.: Dineen, Seán. Complex analysis on infinite-dimensional spaces. Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, 1999.MR 1705327 (2001a:46043)
10.: Floret, Klaus. Natural norms on symmetric tensor products of normed spaces, Note Mat. 17 (1997), 153-188. MR 1749787 (2001g:46038)
11.: -, On ideals of -homogeneous polynomials on Banach spaces, in Topological algebras with applications to differential geometry and mathematical physics (Athens, 1999), pages 19-38. Univ. Athens, Athens, 2002. MR 2000732 (2004i:46075)
12.: Grothendieck, Alexandre. Résumé de la théorie métrique des produits tensoriels topologiques; Bol. Soc. Mat. São Paulo 8 (1956), 83-110. MR 0094682 (20:1194)
13.: John, Kamil. Tensor product of several spaces and nuclearity, Math. Ann. 269 (1984), no. 3, 333-356. MR 0761310 (86b:46119)
14.: -, Tensor powers of operators and nuclearity, Math. Nachr. 129 (1986), 115-121. MR 0864627 (87m:46147)
15.: Kirwan, Padraig and Ryan, Ray. Extendibility of homogeneous polynomials on Banach spaces, Proc. Amer. Math. Soc. 126 (1992), 1023-1029. MR 1415346 (98f:46042)
16.: Pérez-García, David. A counterexample using 4-linear forms, Bull. Aust. Math. Soc. 70 (2004), no. 3, 469-473.MR 2103978 (2005g:46088)
17.: Pisier, Gilles. Counterexamples to a conjecture of Grothendieck, Acta Math. 151 (1983) 181-208. MR 0723009 (85m:46017)

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Daniel Carando
Affiliation: Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, B1644BID Victoria, Buenos Aires, Argentina
Address at time of publication: Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Email: daniel@udesa.edu.ar, dcarando@dm.uba.ar

Verónica Dimant
Affiliation: Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, B1644BID Victoria, Buenos Aires, Argentina
Email: vero@udesa.edu.ar

DOI: 10.1090/S0002-9939-06-08666-7
PII: S 0002-9939(06)08666-7
Keywords: Extendible polynomials, symmetric tensor products, Grothendieck's conjecture
Received by editor(s): August 16, 2005
Received by editor(s) in revised form: February 1, 2006
Posted: November 7, 2006
Additional Notes: The first author was partially supported by CONICET Resolución No. 1584-04, UBACyT Grant X058 and ANPCyT PICT 03-15033.
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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