Multilinear extensions of grothendieck's theorem

Quarterly Journal of Mathematics

Volumn 55, Issue 4, 2004, Pages 441-450

  Bombal, Fernando ^a   Pérez García, David ^a   Villanueva, Ignacio ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10844255602     PISSN: 00335606     EISSN: None     Source Type: Journal    
DOI: 10.1093/qmath/hah017     Document Type: Article

References (23)

1. R. Alencar and M. C. Matos, Some Classes of Multilinear Mappings Between Banach Spaces, Publicaciones del Departamento de Análisis Matemático, sec. 1, no. 12, Universidad Complutense de Madrid, 1989.
2. R. C. Blei, Multilinear measure theory and the Grothendieck factorization theorem, Proc. London Math. Soc. 56 (1988), 529-546.
3. G. Botelho, Cotype and absolutely summing multilinear mappings and homogeneous polynomials, Proc. R. Irish Acad. A97 (1997), 145-153.
4. T. K. Carne, Banach lattices and extensions of Grothendieck's inequality, J. London Math. Soc. 21 (1980), 496-516.
5. Y. S. Choi, S. G. Kim, Y. Meléndez, and A. Tonge, Estimates for absolutely summing norms of polynomials and multilinear maps, Quart. J. Math. 52 (2001), 1-12.
6. A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland, Amsterdam, 1993.
7. J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge University Press, Cambridge, 1995.
8. V. Dimant, Strongly p-summing multilinear operators, J. Math. Anal. Appl. 278 (2003), 182-193.
9. A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. Sao Paulo 8 (1956), 1-79.
10. U. Haagerup, The best constants in the Khintchine inequality, Studia Math. 70 (1982), 231-283.
11. J. L. Krivine, Théorèmes de factorization dans les espaces réticulés, École Polytechnique Palaiseau, Sém. Maurey-Schwartz 1973/74, Exp. XXII, XXIII.
12. p-spaces and their applications, Studio Math. 29 (1968), 257-326.
13. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, Berlin, 1977.
14. M. C. Matos, Absolutely summing holomorphic mappings, An. Acad. Bras. Ci. 68 (1996), 1-13.
15. D. Pérez-García, Some multilinear generalizations of Grothendieck's theorem, preprint.
16. D. Pérez-García and I. Villanueva, Multiple summing operators on Banach spaces, J. Math. Anal. Appl. 285 (2003), 86-96.
17. D. Pérez-García and I. Villanueva, Multiple summing operators on C(K) spaces, Ark. Mat. 42 (2004), 153-171.
18. A. Pietsch, Absolut p-summierende Abbildungen in normierten Räumen, Studia Math. 28 (1967), 333-353.
19. A. Pietsch, Ideals of multilinear functionals (designs of a theory), Proceedings of the Second International Conference on Operator Algebras, Ideals, and their Applications in Theoretical Physics (Leipzig), Teubner-Texte, 1983, 185-199.
20. G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conference Series 60, American Mathematical Society, Providence, 1986.
21. M. S. Ramanujan and E. Schock, Operator ideals and spaces of bilinear operators, Linear and Multilinear Algebra 18 (1985), 307-318.
22. H. H. Schaefer, Banach Lattices and Positive Operators, Springer, Berlin, 1974.
23. A. Tonge, The Von Neumann inequality for polynomials in several Hubert-Schmidt operators, J. London Math. Soc. 18 (1978), 519-526.