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Extension of bilinear forms on Banach spaces


Castillo, Jesús M.F. and García, R. and Jaramillo Aguado, Jesús Ángel (2001) Extension of bilinear forms on Banach spaces. Proceedings of the American Mathematical Society, 129 (12). pp. 3647-3656. ISSN 0002-9939

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We study the extension of bilinear and multilinear forms from a given subspace of a Banach space to the whole space. Precisely, an isomorphic embedding j : E --> X is said to be (linearly) N-exact if N-linear forms on E can be (linear and continuously) extended to X through j. We present some necessary and sufficient conditions for j to be 2-exact, as well as several examples of 2-exact embeddings. We answer a problem of Zalduendo: in a cotype 2 space bilinear extendable and integral forms coincide.

Item Type:Article
Uncontrolled Keywords:Bilinear forms; tensor product; cotype-2 space; embedding
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16650

R. Aron and P. Berner, A Hahn-Banach extension theorem for analytic mapping, Bull. Soc. Math. France 106 (1978), 3-24. MR 80e:46029

F. Blasco, Complementation in spaces of symmetric tensor products and polynomials, Studia Math. 123 (1997), 165-173. MR 98d:46043

J. Bourgain, New classes of Lp-spaces, Lecture Notes in Mathematics 889, Springer, Berlin and New York, 1991. MR 83j:46028

F. Cabello S anchez, J.M.F. Castillo and R. Garc ia, Polynomials on dual isomorphic spaces, Ark. Mat. 38 (2000), 37-44. CMP 2000:11

F. Cabello S anchez, R. Garc ia and I. Villanueva, Extension of multilinear operators on Banach spaces, Extracta Math. 15 (2000), 291-334.

D. Carando, Extendible polynomials on Banach spaces, J. Math. Anal. and Appl. 233 (1999), 359-372. MR 2000d:46057

D. Carando and I. Zalduendo, A Hahn-Banach theorem for integral polynomials, Proc. Amer. Math. Soc. 127 (1999), 241-250. MR 99b:46067

J.M.F. Castillo and M. Gonz ales, Three-space problems in Banach space theory, Lecture Notes in Mathematics 1667, Springer 1997. MR 99a:46034

A. Defant and K. Floret, Tensor norms and Operator ideals, North-Holland Math. Stud., 176, 1993. MR 94e:46130

S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud., 57, 1981. MR 84b:46050

S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer Monographs in Math., Springer, 1999. CMP 99:17

J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge Tracts in Mathematics 43, Cambridge Univ. Press. 1995. MR 96i:46001

P. Galindo, D. Garc ia, M. Maestre and J. Mujica, Extension of multilinear mappings on Banach spaces, Studia Math. 108 (1994), 55-76. MR 95f:46072

E. Hilton and K. Stammbach, A course in homological algebra, Graduate Texts in Mathematics 4, Springer-Verlag. MR 97k:18001

H. Jarchow, On Hilbert-Schmidt spaces, Rendiconti CircoloMat. di Palermo (Suppl.) II (1982), 153-160. MR 84d:46017

N. Kalton, Locally complemented subspaces and Lp-spaces for 0 < p < 1, Math. Nachr. 115 (1984), 71-97. MR 86h:46006

N. Kalton and N.T. Peck, Twisted sums of sequence spaces and the three-space problem, Trans. Amer. Math. Soc. 255 (1979), 1-30. MR 82g:46021

P. Kirwan and R. Ryan, Extendibility of homogeneous polynomials on Banach spaces, Proc. Amer. Math. Soc. 126 (1998), 1023-1029. MR 98f:46042

J. Lindenstrauss, On a certain subspace of l1, Bull. Polish Acad. Sci. 12 (1964), 539-542. MR 30:5153

J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Sequence spaces, Springer, 1977. MR 58:17766

G. Pisier, Counterexamples to a conjecture of Grothendieck, Acta Mat. (1983), 181-208. MR 85m:46017 License or copyright restrictions may apply to redistribution; see 3656 J. M. F. CASTILLO, R. GARC IA, AND J. A. JARAMILLO

R. Ryan, Dunford-Pettis properties, Bull. Polish Acad. Sci. 27 (1979), 373-379. MR 80m:46018

I. Zalduendo, Extending polynomials - a survey, Pub. Dept. An al. Mat. Univ. Complutense Madrid, 41.

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