Publication: A composition theorem for multiple summing operators
Loading...
Full text at PDC
Publication Date
2005-11
Authors
Villanueva, Ignacio
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Wien
Abstract
We prove that the composition S(u(1),..., u(n)) of a multilinear multiple 2-summing operator S with 2-summing linear operators u(j) is nuclear, generalizing a linear result of Grothendieck.
Description
UCM subjects
Unesco subjects
Keywords
Citation
[1] R. Alencar, Multilinear mappings of nuclear and integral type, Proc. Amer. Math. Soc. 94 (1985), no. 1, 33–38.
[2] F. Bombal, D. P´erez-Garc´ıa, and I. Villanueva, Multilinear extensions of Grothendieck’s theorem, to appear in Q. J. Math.
[3] A. Defant and K. Floret, Tensor norms and operator ideals, North-Holland, 1993.
[4] J. Diestel, H. Jarchow, and A. Tonge, Absolutely summing operators, Cambridge Univ. Press, 1995.
[5] J. Diestel and J.J. Uhl, Vector measures, Mathematical Surveys and Monographs, no. 15, Amer. Math. Soc., 1977.
[6] S. Dineen, Complex analysis in locally convex spaces, North-Holland, 1981.
[7] A. Grothendieck, Produits tensoriels topologiques et espaces nucl´eaires, Mem. Amer. Math. Soc. 16 (1955).
[8] M.C. Matos, Fully absolutely summing and Hilbert-Schmidt multilinear mappings, Collect. Math. 54 (2003), 111–136.
[9] D. P´erez-Garc´ıa, The inclusion theorem for multiple summing operators, Preprint.
[10] D. P´erez-Garc´ıa and I. Villanueva, Multiple summing operators on Banach spaces, J. Math. Anal. Appl. 285 (2003), 86–96.
[11] D. P´erez-Garc´ıa and I. Villanueva, Multiple summing operators on C(K) spaces, To appear in Ark. Mat.
[12] I. Villanueva, Integral mappings between Banach spaces, J. Math. Anal. Appl. 279 (2003), 56–70.