Hahn-Banach extension of multilinear forms and summability

Journal of Mathematical Analysis and Applications

Volumn 336, Issue 2, 2007, Pages 1161-1177

  Jarchow, H ^a   Palazuelos, C ^b   Perez Garcia D ^c   Villanueva, I ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^c UNIVERSIDAD REY JUAN CARLOS   (Spain)

Author keywords

Bilinear forms; Hahn Banach extension; Multilinear forms; Summing properties

Indexed keywords

EID: 34548095953     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.03.057     Document Type: Article

References (39)

1. R. Alencar, M.C. Matos, Some classes of multilinear mappings between Banach spaces, Publ. Dep. de Análisis Matemático, Sec. 1, no. 12, UCM, 1989
2. Aron R.M., and Berner P.D. A Hahn-Banach extension theorem for analytic mappings. Bull. Soc. Math. France 106 1 (1978) 3-24
3. Blei R.C. Multidimensional extensions of Grothendieck's inequality and applications. Ark. Mat. 17 (1979) 51-68
4. Blei R.C. Multilinear measure theory and the Grothendieck factorization theorem. Proc. London. Math. Soc. 56 3 (1988) 529-546
5. Bombal F., Villanueva I., and Pérez-García D. Multilinear extensions of Grothendieck's theorem. Q. J. Math. 55 (2004) 441-450
6. ∞. Acta Math. 152 (1984) 1-48
7. ∞ and bounded bianalytic functions. Trans. Amer. Math. Soc. 286 (1984) 313-337
8. Cabello F., Pérez-García D., and Villanueva I. Unexpected subspaces of tensor products. J. London. Math. Soc. (2) 74 2 (2006) 512-526
9. Carando D. Extendible polynomials on Banach spaces. J. Math. Anal. Appl. 233 (1999) 359-372
10. D. Carando, V. Dimant, Extension of polynomials and John's theorem for symmetric tensor products, Proc. Amer. Math. Soc., in press
11. Carne T.K. Banach lattices and extensions of Grothendieck's inequality. J. London Math. Soc. 21 (1980) 496-516
12. Casazza P., and Nielsen N.J. The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures. Studia Math. 155 (2003) 1-21
13. Castillo J.M.F., García R., and Jaramillo J. Extension of bilinear forms on Banach spaces. Proc. Amer. Math. Soc. 129 12 (2001) 3647-3656
14. 1-spaces. Ann. Acad. Sci. Fenn. Math. 27 (2002) 91-96
15. Choi Y.S., Kim S.G., Meléndez Y., and Tonge A. Estimates for absolutely summing norms of polynomials and multilinear maps. Q. J. Math. 52 (2001) 1-12
16. Davie A.M., and Gamelin T.W. A theorem on polynomial-star approximation. Proc. Amer. Math. Soc. 106 2 (1989) 351-356
17. Defant A., and Floret K. Tensor Norms and Operator Ideals (1993), North-Holland, Amsterdam
18. 1-spaces, Houston J. Math., in press
19. Diestel J., Jarchow H., and Tonge A. Absolutely Summing Operators. Cambridge Stud. Adv. Math. vol. 43 (1995), Cambridge Univ. Press, Cambridge
20. Dineen S. Holomorphically complete locally convex topological vector spaces. Lecture Notes in Math. vol. 332 (1973) 77-111
21. Galindo P., García D., Maestre M., and Mújica J. Extension of multilinear mappings on Banach spaces. Studia Math. 108 1 (1994) 55-76
22. S. Geiss, Ideale multilinearer Abbildungen, Diplomarbeit Universität Jena, 1984
23. Gordon Y., and Lewis D.R. Absolutely summing operators and local unconditional structures. Acta Math. 133 (1974) 27-48
24. Gordon Y., Lewis D.R., and Retherford J.R. Banach ideals of operators with applications to the finite dimensional structure of Banach spaces. Israel J. Math. 13 (1972) 348-360
25. Jarchow H. On Hilbert-Schmidt spaces. Rend. Circ. Mat. Palermo (Suppl.) II (1982) 153-160
26. Kirwan P., and Ryan R.A. Extendibility of homogeneous polynomials on Banach spaces. Proc. Amer. Math. Soc. 126 4 (1998) 1023-1029
27. Matos M.C. Fully absolutely summing and Hilbert-Schmidt multilinear mappings. Collect. Math. 54 (2003) 111-136
28. Maurey B. Un théorème de prolongement. C. R. Acad. Sci. Paris Ser. A 279 (1974) 329-332
29. ∞. C. R. Acad. Sci. Paris Ser. A 279 (1974) 9-12
30. Pérez-García D. A counterexample using 4-linear forms. Bull. Austral. Math. Soc. 70 (2004) 469-473
31. Pérez-García D. Comparing different classes of absolutely summing multilinear operators. Arch. Math. (Basel) 85 (2005) 258-267
32. Pérez-García D. The trace class is a Q-algebra. Ann. Acad. Sci. Fenn. Math. 31 2 (2006) 287-295
33. Pietsch A. Operator Ideals (1980), North-Holland, Amsterdam
34. Pietsch A. Ideals of multilinear functionals (designs of a theory). Proc. 2nd Int. Conf. on Operator Algebras, Ideals and their Applications in Theoretical Physics. Leipzig. Teubner-Texte (1983) 185-199
35. Pisier G. Factorization of Linear Operators and Geometry of Banach Spaces. CBMS vol. 60 (1985), Amer. Math. Soc., Providence, RI
36. Tonge A. The Von Neumann inequality for polynomials in several Hilbert-Schmidt operators. J. London Math. Soc. 18 (1978) 519-526
37. Meléndez Y., and Tonge A. Polynomials and the Pietsch domination theorem. Math. Proc. R. Ir. Acad. A 99 2 (1999) 195-212
38. Wojtaszczyk P. Banach Spaces for Analysts. Cambridge Stud. Adv. Math. vol. 25 (1991), Cambridge Univ. Press, Cambridge
39. Zalduendo I. Extending polynomials on Banach spaces-A survey. Rev. Un. Mat. Argentina 46 2 (2005) 45-72