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Multiple Weakly Summing Multilinear Mappings and Polynomials
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Abstract
In this paper, we introduce and study a new class containing absolutely summing multilinear mappings and polynomials, which we call multiple weakly summing multilinear mappings and polynomials. We investigate some interesting properties about multiple weakly (p; q1, · · · , qk)-summing multilinear mappings and polynomials defined on Banach spaces: In particular, we prove a kind of Dvoretzky-Rogers’ Theorem and an ideal property for multiple weakly (p; q1, · · · , qk)-summing multilinear mappings and polynomials. We also prove that the Aron-Berner extensions of multiple weakly (p; q1, · · · , qk)- summing multilinear mappings and polynomials are also multiple weakly (p; q1, · · · , qk)- summing.
참고문헌 (7)
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- J. Diestel, "Absolutely Summing Operators" (1995), Cambridge University Press, Cambridge
- S. Dineen, "Complex Analysis on Infinite Dimensional Spaces" (1999), Springer-Verlag, London
- M. Matos, "The Dvoretzky-Rogers theorem for polynomial and multilinear mappings", pp.849~856 (1997), in ¡±45o. Seminario Brasileiro de Analise, Florianop
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