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