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

 

Extension of polynomials and John's theorem for symmetric tensor products


Authors: Daniel Carando and Verónica Dimant
Journal: Proc. Amer. Math. Soc. 135 (2007), 1769-1773
MSC (2000): Primary 46G25, 46B28
Published electronically: November 7, 2006
MathSciNet review: 2286087
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Abstract: We show that for every infinite-dimensional normed space $ E$ and every $ k\geq 3$ there are extendible $ k$-homogeneous polynomials which are not integral. As a consequence, we prove a symmetric version of a result of John.


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Additional Information

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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.