On Ideals of Polynomials and Their Applications
نویسنده
چکیده
The notion of operators ideals goes back to Grothendieck [10] and its natural extension to polynomials and multilinear mappings is credited to Pietsch [24]. We prove some results on ideals of polynomials and obtain, as corollaries and particular cases, new properties concerning dominated, almost summing, integral polynomials and related ideals. Among other results, we obtain Extrapolation and DvoretzkyRogers type theorems for special ideals of polynomials, and prove new characterizations of L∞-spaces, extending results of Stegall-Retherford [26] and Cilia-D’Anna-Gutiérrez [6]. Throughout this paper E,E1, ..., En, F,G,G1, ..., Gn, H will stand for (real or complex) Banach spaces. Given a natural number n ≥ 2, the Banach spaces of all continuous n-linear mappings from E1 × ... × En into F endowed with the sup norm will be denoted by L(E1, ..., En;F ) and the Banach space of all continuous n-homogeneous polynomials P from E into F with the sup norm is denoted
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