On null sequences for Banach operator ideals, trace duality and approximation properties
Let A be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of A-null sequences of Carl and Stephani on X, c0,A(X), from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of th...
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| Lenguaje: | Inglés |
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Wiley-VCH Verlag
2017
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 08665caa a22008537a 4500 | ||
|---|---|---|---|
| 001 | PAPER-15400 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230607131904.0 | ||
| 008 | 190410s2017 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85017445453 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Lassalle, S. | |
| 245 | 1 | 3 | |a On null sequences for Banach operator ideals, trace duality and approximation properties |
| 260 | |b Wiley-VCH Verlag |c 2017 | ||
| 270 | 1 | 0 | |m Lassalle, S.; Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID), Argentina; email: slassalle@udesa.edu.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Ain, K., Lillemets, R., Oja, E., Compact operators which are defined by ℓp-spaces (2012) Quaest. Math., 35, pp. 145-159 | ||
| 504 | |a Ain, K., Oja, E., A description of relatively (p;r)-compact sets (2012) Acta Comment. Univ. Tartu. Math., 16, pp. 227-232 | ||
| 504 | |a Ain, K., Oja, E., On (p,r)-null sequences and their relatives (2015) Math. Nachr., 288, pp. 1569-1580 | ||
| 504 | |a Carl, B., Stephani, I., On A-compact operators, generalized entropy numbers and entropy ideals (1984) Math. Nachr., 199, pp. 77-95 | ||
| 504 | |a Choi, Y.S., Kim, J.M., The dual space of (L(X,Y);τp) and the p-approximation property (2010) J. Funct. Anal., 259, pp. 2437-2454 | ||
| 504 | |a Defant, A., Floret, K., (1993) Tensor Norms and Operators Ideal, , North-Holland Publishing Co., Amsterdam | ||
| 504 | |a Delgado, J.M., Oja, E., Piñeiro, C., Serrano, E., The p-approximation property in terms of density of finite rank operators (2009) J. Math. Anal. Appl., 354, pp. 159-164 | ||
| 504 | |a Delgado, J.M., Piñeiro, C., Serrano, E., Density of finite rank operators in the Banach space of p-compact operators (2010) J. Math. Anal. Appl., 370, pp. 498-505 | ||
| 504 | |a Diestel, J., Fourie, J.H., Swart, J., (2008) The Metric Theory of Tensor Products, Grothendieck's résumé revisited, , American Mathematical Society, Providence, RI | ||
| 504 | |a Diestel, J., Jarchow, H., Tonge, A., (1995) Absolutely Summing Operators. Cambridge Studies in Advanced Mathematics, 43. , Cambridge University Press, Cambridge | ||
| 504 | |a Fourie, J., Swart, J., Banach ideals of p-compact operators (1979) Manuscripta Math., 26, pp. 349-362 | ||
| 504 | |a Fourie, J., Swart, J., Tensor products and Banach ideals of p-compact operators (1981) Manuscripta Math., 35, pp. 343-351 | ||
| 504 | |a Galicer, D., Lassalle, S., Turco, P., The ideal of p-compact operators: a tensor product approach (2012) Studia Math., 211, pp. 269-286 | ||
| 504 | |a Gordon, Y., Lewis, D., Retheford, J., Banach ideals of operators with applications (1973) J. Funct. Anal., 14, pp. 85-129 | ||
| 504 | |a Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires (1955) Memoirs of the American Mathematical Society, 16, p. 140 | ||
| 504 | |a Jarchow, H., Ott, R., On trace ideals (1982) Math. Nachr., 108, pp. 23-37 | ||
| 504 | |a Kim, J.M., Unconditionally p-null sequences and uncoditionally p-compact operators (2014) Studia Math., 224, pp. 133-142 | ||
| 504 | |a Kim, J.M., The Kup-approximation property and its duality (2015) J. Aust. Math. Soc., 98, pp. 364-374 | ||
| 504 | |a Kim, J.M., Duality between the K1- and the Ku1-approximation properties, , To appear in Houston J. Math | ||
| 504 | |a Lassalle, S., Oja, E., Turco, P., Weaker relatives of the bounded approximation property for a Banach operator ideal (2016) J. Approx. Theory, 205, pp. 25-42 | ||
| 504 | |a Lassalle, S., Turco, P., On p-compact mappings and the p-approximation properties (2012) J. Math. Anal. Appl., 389, pp. 1204-1221 | ||
| 504 | |a Lassalle, S., Turco, P., The Banach ideal of A-compact operators and related approximation properties (2013) J. Funct. Anal., 265, pp. 2452-2464 | ||
| 504 | |a Lima, A., Lima, V., Oja, E., Bounded approximation properties via integral and nuclear operators (2010) Proc. Amer. Math. Soc., 138, pp. 287-297 | ||
| 504 | |a Lindenstrauss, J., On a certain subspace of ℓ1 (1964) Bull. Acad. Pol. Sci., Sr. Sci. Math. Astron. Phys., 12, pp. 539-542 | ||
| 504 | |a Lindenstrauss, J., Tzafriri, L., (1977) Classical Banach Spaces I. Vol. 92, , Springer-Verlag, Berlin, New York | ||
| 504 | |a Oertel, F., Local properties of accessible injective operator ideals (1998) Czechoslovak Math. J., 48 (123), pp. 119-133 | ||
| 504 | |a Oja, E., Inner and outer inequalities with applications to approximation properties (2011) Trans. Amer. Math. Soc., 363, pp. 5827-5846 | ||
| 504 | |a Oja, E., A remark on the approximation of p-compact operators by finite-rank operators (2012) J. Math. Anal. Appl., 387, pp. 949-952 | ||
| 504 | |a Oja, E., Grothendieck's nuclear operator theorem revisited with an application to p-null sequences (2012) J. Funct. Anal., 263, pp. 2876-2892 | ||
| 504 | |a Pietsch, A., (1980) Operators Ideals, , North-Holland Publishing Company, Amsterdam/New York/Oxford | ||
| 504 | |a Pietsch, A., The ideal of p-compact operators and its maximal hull (2014) Proc. Amer. Math. Soc., 142, pp. 519-530 | ||
| 504 | |a Piñeiro, C., Delgado, J.M., p-convergent sequences and Banach spaces in which p-compact sets are q-compact (2011) Proc. Amer. Math. Soc., 139, pp. 957-967 | ||
| 504 | |a Ryan, R., (2002) Introduction to Tensor Products on Banach Spaces, , Springer, London | ||
| 504 | |a Sinha, D.P., Karn, A.K., Compact operators whose adjoints factor trough subspaces of ℓp (2002) Studia Math., 150, pp. 17-33 | ||
| 504 | |a Turco, P., A-compact mappings (2015) Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 110, pp. 863-880 | ||
| 520 | 3 | |a Let A be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of A-null sequences of Carl and Stephani on X, c0,A(X), from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when A is right-accessible for (ℓ1;X),c0,A(X) behaves much alike c0(X). When this is the case we give a geometric tensor product representation of c0,A(X). On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of c0,A(X). We apply our results to study some problems related with the KA -approximation property giving a trace condition which is used to solve the remaining case (p=1) of a problem posed by Kim (2015). Namely, we prove that if a dual space has the K1 -approximation property then the space has the Ku,1 -approximation property. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim |l eng | |
| 536 | |a Detalles de la financiación: PIP 0483 | ||
| 536 | |a Detalles de la financiación: 1-474, UBACyT, PICT-2015-2299 | ||
| 536 | |a Detalles de la financiación: This project was supported in part by CONICET PIP 0483, ANPCyT PICT-2015-2299 and UBACyT 1-474. The authors would like to thank J.?M.?Kim for sending to them a preliminary and the final version of. Also, the authors are grateful to the referees for their careful reading and suggestions which helped them to improve the presentation of this article. | ||
| 593 | |a Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID), Victoria, Buenos Aires, Argentina | ||
| 593 | |a IMAS – CONICET, Argentina | ||
| 593 | |a IMAS - UBA - CONICET - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina | ||
| 690 | 1 | 0 | |a 46B45; SECONDARY: 46B28 |
| 690 | 1 | 0 | |a 46B50 |
| 690 | 1 | 0 | |a APPROXIMATION PROPERTIES |
| 690 | 1 | 0 | |a COMPACT SETS |
| 690 | 1 | 0 | |a NULL SEQUENCES |
| 690 | 1 | 0 | |a OPERATOR IDEALS |
| 690 | 1 | 0 | |a PRIMARY: 46B04 |
| 700 | 1 | |a Turco, P. | |
| 773 | 0 | |d Wiley-VCH Verlag, 2017 |g v. 290 |h pp. 2308-2321 |k n. 14-15 |p Math. Nachr. |x 0025584X |t Mathematische Nachrichten | |
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| 856 | 4 | 0 | |u https://doi.org/10.1002/mana.201600273 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_0025584X_v290_n14-15_p2308_Lassalle |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0025584X_v290_n14-15_p2308_Lassalle |y Registro en la Biblioteca Digital |
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