Abstract:
We study extendibility of diagonal multilinear operators from ℓp to ℓq spaces.We determine the values of p and q for which every diagonal n-linear operator is extendible, and those for which the only extendible ones are integral. We address the same question for multilinear forms on ℓp. © 2013 Springer-Verlag Italia.
Registro:
Documento: |
Artículo
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Título: | Diagonal extendible multilinear operators between ℓp-spaces |
Autor: | Carando, D.; Dimant, V.; Sevilla-Peris, P.; Villafañe, R. |
Filiación: | Departamento de Matemática, Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, IMAS, CONICET, C1428EGA Buenos Aires, Argentina Departamento de Matemática, Universidad de San Andrés, CONICET, Vito Dumas 284, Victoria, B1644BID Buenos Aires, Argentina Instituto Universitario de Matemática Pura y Aplicada and DMA, ETSIAMN, Universitat Politècnica de València, Cmno Vera s/n, 46022 Valencia, Spain
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Palabras clave: | Extension of multilinear operators; Multilinear mappings; Sequence spaces |
Año: | 2014
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Volumen: | 108
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Número: | 2
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Página de inicio: | 541
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Página de fin: | 555
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DOI: |
http://dx.doi.org/10.1007/s13398-013-0125-7 |
Título revista: | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
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Título revista abreviado: | Revista Real Academia Ciencias Exactas, Fisicas Naturales - Serie A: Matematicas
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ISSN: | 15787303
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15787303_v108_n2_p541_Carando |
Referencias:
- Alencar, R., Multilinear mappings of nuclear and integral type (1985) Proc. Am. Math. Soc., 94 (1), pp. 33-38
- Alencar, R., Matos, M., Some classes of multilinear mappings between Banach spaces (1989) Pub. Dep. An. Mat. Univ. Complut. Madrid, p. 12
- Blei, R.C., Multilinear measure theory and the Grothendieck factorization theorem (1988) Proc. Lond. Math. Soc, 56 (3), pp. 529-546
- Bohnenblust, H.F., Hille, E., On the absolute convergence of Dirichlet series (1931) Ann. Math. (2), 32 (3), pp. 600-622
- Botelho, G., Braunss, H., Junek, H., Pellegrino, D., Holomorphy types and ideals of multilinear mappings (2006) Studia Math, 177, pp. 43-65
- Botelho, G., Michels, C., Pellegrino, D., Complex interpolation and summability properties of multilinear operators (2010) Rev. Mat. Complut, 23 (1), pp. 139-161
- Botelho, G., Pellegrino, D., Two new properties of ideals of polynomials and applications (2005) Indag. Math. (N. S.), pp. 16157-16169
- Botelho, G., Pellegrino, D., When every multilinear mapping is multiple summing (2009) Math. Nachr, 282 (10), pp. 1414-1422
- Çalişkan, E., Pellegrino, D., On the multilinear generalizations of the concept of absolutely summing operators (2007) Rocky Mt. J. Math, 37, pp. 1137-1154
- Carando, D., Extendibility of polynomials and analytic functions on ℓp (2001) Studia Math., 145 (1), pp. 63-73
- Carando, D., Dimant, V., Muro, S., Coherent sequences of polynomial ideals on Banach spaces (2009) Math. Nachr, 282 (8), pp. 1111-1133
- Carando, D., Dimant, V., Sevilla-Peris, P., Limit orders and multilinear forms on ℓp spaces (2006) Publ. Res. Inst. Math. Sci, 42 (2), pp. 507-522
- Carando, D., Dimant, V., Sevilla-Peris, P., Multilinear Hölder-type inequalities on Lorentz sequence spaces (2009) Studia Math, 195 (2), pp. 127-146
- Carando, D., Lassalle, S., Extension of vector-valued integral polynomials (2005) J. Math. Anal. Appl, 307 (1), pp. 77-85
- Carando, D., Sevilla-Peris, P., Extendibility of bilinear forms on Banach sequence spaces Israel J. Math, , arXiv: 1212. 0777 (to appear)
- Castillo, J., García, R., Jaramillo, J.A., Extension of bilinear forms on Banach spaces (2001) Proc. Am. Math. Soc, 129 (12), pp. 3647-3656
- Carl, B., A remark on p-integral and p-absolutely summing operators from ℓu into ℓv (1976) Studia Math., 57 (3), pp. 257-262
- Defant, A., Floret, K., (1993) Tensor norms and operator ideals, , North Holland, Amsterdam
- Diestel, J., Jarchow, H., Tonge, A., (1995) Absolutely summing operators, , Cambridge University Press, Cambridge
- Dineen, S., (1999) Complex analysis on infinite dimensional spaces, , Springer-Verlag, London
- Jarchow, H., Palazuelos, C., Pérez-García, D., Villanueva, I., Hahn-Banach extension of multilinear forms and summability (2007) J. Math. Anal. Appl, 336 (2), pp. 1161-1177
- Kirwan, P., Ryan, R., Extendibility of homogeneous polynomials on Banach spaces (1998) Proc. Am. Math. Soc, 126 (4), pp. 1023-1029
- König, H., Diagonal and convolution operators as elements of operator ideals (1975) Math. Ann., 218 (2), pp. 97-106
- Lindenstrauss, J., Tzafriri, L., (1977) Classical Banach spaces II, , Springer, Berlin
- Matos, M., Absolutely summing holomorphic mappings (1996) An. Acad. Bras. Ci., 68, pp. 1-13
- Maurizi, B., Queffélec, H., Some remarks on the algebra of bounded Dirichlet series (2010) J. Fourier Anal. Appl, 16 (5), pp. 676-692
- Mujica, J., (1986) Complex analysis in Banach spaces. North-Holland mathematics studies, 120. , North-Holland
- Pérez-García, D., Comparing different classes of absolutely summing multilinear operators (2005) Arch. Math. (Basel), 85 (3), pp. 258-267
- García Pérez, D., The trace class is a Q-algebra (2006) Ann. Acad. Sci. Fenn. Math, 31 (2), pp. 287-295
- Pietsch, A., (1978) Operator ideals. Mathematische monographien (Mathematical monographs), p. 16. , VEB Deutscher Verlag der Wissenschaften, Berlin
- Pisier, G., Counterexamples to a conjecture of Grothendieck (1983) Acta Math, 151 (3-4), pp. 181-208
- Ryan, R., (2002) Introduction to tensor products of Banach spaces. Springer monographs in mathematics, , Springer-Verlag, London
- Villanueva, I., Integral mappings between Banach spaces (2003) J. Math. Anal. Appl., 279 (1), pp. 56-70
Citas:
---------- APA ----------
Carando, D., Dimant, V., Sevilla-Peris, P. & Villafañe, R.
(2014)
. Diagonal extendible multilinear operators between ℓp-spaces. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 108(2), 541-555.
http://dx.doi.org/10.1007/s13398-013-0125-7---------- CHICAGO ----------
Carando, D., Dimant, V., Sevilla-Peris, P., Villafañe, R.
"Diagonal extendible multilinear operators between ℓp-spaces"
. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 108, no. 2
(2014) : 541-555.
http://dx.doi.org/10.1007/s13398-013-0125-7---------- MLA ----------
Carando, D., Dimant, V., Sevilla-Peris, P., Villafañe, R.
"Diagonal extendible multilinear operators between ℓp-spaces"
. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, vol. 108, no. 2, 2014, pp. 541-555.
http://dx.doi.org/10.1007/s13398-013-0125-7---------- VANCOUVER ----------
Carando, D., Dimant, V., Sevilla-Peris, P., Villafañe, R. Diagonal extendible multilinear operators between ℓp-spaces. Revista Real Academia Ciencias Exactas, Fisicas Naturales - Serie A: Matematicas. 2014;108(2):541-555.
http://dx.doi.org/10.1007/s13398-013-0125-7