Absolutely summing polynomials on Banach spaces with unconditional basis |
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Authors: | Geraldo Botelho Daniel Pellegrino |
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Institution: | a Faculdade de Matemática, Universidade Federal de Uberlândia, Cep 38400-902, Uberlândia, MG, Brazil b Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, CEP 58109-970, Campina Grande, PB, Brazil |
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Abstract: | If X is a Banach space with a normalized unconditional Schauder basis (xn), we define whenever and obtain estimates for μX,(xn) when every continuous m-homogeneous polynomial from X into Y is absolutely (q,1) summing. Our results provide new information on coincidence situations between the space of absolutely summing m-homogeneous polynomials and the whole space of continuous m-homogeneous polynomials. In particular, when m=1, we obtain new contributions to the linear theory of absolutely summing operators. |
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Keywords: | Polynomials Multilinear mappings Absolutely summing operators Cotype |
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