Villanueva, Ignacio and Pérez García, David (2005) A composition theorem for multiple summing operators. Monatshefte fur Mathematik, 146 (3). pp. 257361. ISSN 00269255

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Abstract
We prove that the composition S(u(1),..., u(n)) of a multilinear multiple 2summing operator S with 2summing linear operators u(j) is nuclear, generalizing a linear result of Grothendieck.
Item Type:  Article 

Uncontrolled Keywords:  Multilinear operators; Multiple psumming operators; Nuclear operators 
Subjects:  Sciences > Mathematics > Mathematical analysis 
ID Code:  11661 
References:  [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´erezGarc´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, NorthHolland, 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, NorthHolland, 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 HilbertSchmidt multilinear mappings, Collect. Math. 54 (2003), 111–136. [9] D. P´erezGarc´ıa, The inclusion theorem for multiple summing operators, Preprint. [10] D. P´erezGarc´ıa and I. Villanueva, Multiple summing operators on Banach spaces, J. Math. Anal. Appl. 285 (2003), 86–96. [11] D. P´erezGarc´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. 
Deposited On:  03 Dec 2010 08:45 
Last Modified:  03 Dec 2014 08:43 
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