Weakly Compact and Absolutely Summing Polynomials |
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Authors: | Geraldo Botelho |
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Affiliation: | Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902, Uberlândia, Brazilf1botelho@ufu.brf1 |
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Abstract: | This paper shows that, contrary to the case of linear operators, absolutely summing homogeneous polynomials are not always weakly compact. It is also shown that, regardless of the infinite dimensional Banach space E and the positive integer n, there exists an n-homogeneous polynomial P from E to E that plays the role of the identity operator in the sense that P is neither compact nor absolutely r-summing for any r, and P is weakly compact if and only if E is reflexive. |
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Keywords: | homogeneous polynomials weak compactness absolute summability |
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