Abstract of a paper by Adriano Thiago Bernardino, Daniel Pellegrino and Juan B. Seoane-Sepulveda
This is an announcement for the paper "Multiple $(p;q;r)$-summing polynomials and multilinear operators" by Adriano Thiago Bernardino, Daniel Pellegrino and Juan B. Seoane-Sepulveda. Abstract: The concept of absolutely $(p;q;r)$-summing linear operators is due to A. Pietsch; it is a natural extension of the classical notion of absolutely $(p;q)$-summing operators. Very recently D. Achour introduced the concept of absolutely $(p;q;r)$-summing multilinear mappings. In this paper we obtain some properties of this class and show that the polynomial version of this notion is neither coherent nor compatible (according to the definition of Carando, Dimant, and Muro). Here we shall provide an alternative approach that generates coherent and compatible ideals. Archive classification: math.FA Submitted from: dmpellegrino@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.4898 or http://arXiv.org/abs/1109.4898
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alspach@math.okstate.edu