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Abstract:

We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from ε and destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never have the Gordon-Lewis property. In some cases we even obtain that the monomial basic sequence can never be unconditional. Analogous problems for multilinear ideals are addressed, and noteworthy differences between the 2-fold and the n-fold (n ≥ 3) theory are obtained. © 2010 Published by Oxford University Press. All rights reserved.

Registro:

Documento: Artículo
Título:Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
Autor:Carando, D.; Galicer, D.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pab. i, (1428) Buenos Aires, Argentina
Año:2011
Volumen:62
Número:4
Página de inicio:845
Página de fin:869
DOI: http://dx.doi.org/10.1093/qmath/haq024
Título revista:Quarterly Journal of Mathematics
Título revista abreviado:Q. J. Math.
ISSN:00335606
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00335606_v62_n4_p845_Carando

Referencias:

  • Aron, R.M., Cole, B.J., Gamelin, T.W., Spectra of algebras of analytic functions on a Banach space (1991) J. Reine Angew. Math., 415, pp. 51-93
  • Botelho, G., Braunss, H.-A., Junek, H., Pellegrino, D., Holomorphy types and ideals of multilinear mappings (2006) Studia Mathematica, 177 (1), pp. 43-65. , DOI 10.4064/sm177-1-4
  • Carando, D., Extendible polynomials on Banach spaces (1999) J. Math. Anal. Appl., 233, pp. 359-372
  • Carando, D., Extendibility of polynomials and analytic functions on p (2001) Studia Math., 145, pp. 63-73
  • Carando, D., Galicer, D., Natural Symmetric Tensor Norms, , http://arXiv.org/abs/1002.3950, preprint
  • Carandov. Dimant, D., Muro, S., Coherent sequences of polynomial ideals on Banach spaces (2009) Math. Nachr., 282, pp. 1111-1133
  • Carando, D., Dimant, V., Sevilla-Peris, P., Limit orders and multilinear forms on p spaces (2006) Publications of the Research Institute for Mathematical Sciences, 42 (2), pp. 507-522. , DOI 10.2977/prims/1166642113
  • Carandov. Dimant, D., Sevilla-Peris, P., Ideals of multilinear forms-a limit order approach (2007) Positivity, 11, pp. 589-607
  • Carando, D., Dimant, V., Sevilla-Peris, P., Multilinear Hölder-type inequalities on Lorentz sequence spaces (2009) Studia Math., 195, pp. 127-146
  • Casazza, P.G., Shura, T.J., (1989) Tsirelson's Space, Lecture Notes in Mathematics 1363, pp. 8-204. , Springer, Berlin, With an appendix by J. Baker, O. Slotterbeck and R. Aron
  • Defant, A., Diaz, J.C., Garcia, D., Maestre, M., Unconditional Basis and Gordon-Lewis Constants for Spaces of Polynomials (2001) Journal of Functional Analysis, 181 (1), pp. 119-145. , DOI 10.1006/jfan.2000.3702, PII S0022123600937029
  • Defant, A., Floret, K., (1993) Tensor Norms and Operator Ideals, North-Holland Mathematics Studies 176, pp. 11-566. , North-Holland, Amsterdam
  • Defant, A., Kalton, N., Unconditionality in spaces ofm-homogeneous polynomials (2005) Q. J. Math., 56, pp. 53-64
  • Defant, A., Pérez-Garća, D., A tensor norm preserving unconditionality for Lp-spaces (2008) Trans. Amer. Math. Soc., 360, pp. 3287-3306
  • Diestel, J., Jarchow, H., Tonge, A., (1995) Absolutely Summing Operators, , Cambridge Studies in Advanced Mathematics 43, Cambridge University Press, Cambridge
  • Dineen, S., (1999) Complex Analysis on Infinite Dimensional Spaces, pp. 15-543. , Springer Monographs in Mathematics, Springer, London
  • Floret, K., Natural norms on symmetric tensor products of normed spaces (1997) Note Mat., 17, pp. 153-188
  • Floret, K., Minimal ideals of n-homogeneous polynomials on Banach spaces (2001) Results in mathematics, 39 (3-4), pp. 201-217
  • Floret, K., (2001) The Extension Theorem for Norms on Symmetric Tensor Products of Normed Spaces, Recent Progress in Functional Analysis, pp. 225-237. , (eds K. D. Bierstedt et al. ), North-Holland Mathematics Studies 189, Elsevier, Amsterdam
  • Floret, K., (2002) On Ideals of N-homogeneous Polynomials on Banach Spaces, Topological Algebras with Applications to Differential Geometry and Mathematical Physics, pp. 19-38. , P. Strantzalos et al. ) University of Athens, Department of Mathematics, Athens
  • Floret, K., Hunfeld, S., Ultrastability of ideals of homogeneous polynomials and multilinear mappings on Banach spaces (2002) Proc. Amer. Math. Soc., 130, pp. 1425-1435
  • Gordon, Y., Lewis, D.R., Absolutely summing operators and local unconditional structures (1974) Acta Math., 133, pp. 27-48
  • Grecu, B.C., Ryan, R.A., Schauder bases for symmetric tensor products (2005) Publications of the Research Institute for Mathematical Sciences, 41 (2), pp. 459-469
  • Jarchow, H., Palazuelos, C., Pérez-Garća, D., Villanueva, I., Hahn Banach extensions of multilinear forms and summability (2007) J. Math. Anal. Appl., 336, pp. 1161-1177
  • Kirwan, P., Ryan, R.A., Extendibility of homogeneous polynomials on Banach spaces (1998) Proceedings of the American Mathematical Society, 126 (4), pp. 1023-1029
  • Lindenstrauss, J., Tzafriri, L., (1977) Classical Banach Spaces I. Sequence Spaces, Ergebnisse der Mathematik und Ihrer Grenzgebiete, pp. XIII+190. , 92, Berlin, Springer
  • Perez-Garcia, D., The inclusion theorem for multiple summing operators (2004) Studia Mathematica, 165 (3), pp. 275-290
  • Perez-Garcia, D., Villanueva, I., There is no lattice preserving natural tensor norm (2004) Quaestiones Mathematicae, 27 (3), pp. 267-273
  • Perez-Garcia, D., Villanueva, I., Unconditional bases in tensor products of hilbert spaces (2005) Mathematica Scandinavica, 96 (2), pp. 280-288
  • Pisier, G., Some results on Banach spaces without local unconditional structure (1978) Compos. Math., 37, pp. 3-19
  • Schneider, B., On absolutely p-summing and related multilinear mappings, Wiss. Z. Brandenburg (1991) Landeshochsch, 35, pp. 105-117
  • Schütt, C., Unconditionality in tensor products (1978) Israel J. Math., 31, pp. 209-216
  • Schütt, I., Unconditional bases in Banach spaces of absolutely p-summing operators (1990) Math. Nachr., 146, pp. 175-194
  • Tomczak-Jaegermann, N., (1989) Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics 38, pp. 11-395. , Longman Scientific & Technical/Wiley, Harlow/NewYork
  • Tzafriri, L., On Banach spaces with unconditional basis (1974) Israel J. Math., 17, pp. 84-93

Citas:

---------- APA ----------
Carando, D. & Galicer, D. (2011) . Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators. Quarterly Journal of Mathematics, 62(4), 845-869.
http://dx.doi.org/10.1093/qmath/haq024
---------- CHICAGO ----------
Carando, D., Galicer, D. "Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators" . Quarterly Journal of Mathematics 62, no. 4 (2011) : 845-869.
http://dx.doi.org/10.1093/qmath/haq024
---------- MLA ----------
Carando, D., Galicer, D. "Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators" . Quarterly Journal of Mathematics, vol. 62, no. 4, 2011, pp. 845-869.
http://dx.doi.org/10.1093/qmath/haq024
---------- VANCOUVER ----------
Carando, D., Galicer, D. Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators. Q. J. Math. 2011;62(4):845-869.
http://dx.doi.org/10.1093/qmath/haq024