Factorization of (q,p)-summing polynomials through Lorentz spaces

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• 作者：M. Mastyło^a ; ^{mastylo@amu.edu.pl} ; P. Rueda^b ; ^{pilar.rueda@uv.es} ; E.A. Sá ; nchez Pé ; rez^c ; ^{easancpe@mat.upv.es}
• 关键词：Factorization ; Summing polynomials ; Pisier's theorem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：195-206
• 全文大小：365 K
• 卷排序：449

文摘

We present a vector valued duality between factorable (q,p)(q,p)-summing polynomials and (q,p)(q,p)-summing linear operators on symmetric tensor products of Banach spaces. Several applications are provided. First, we prove a polynomial characterization of cotype of Banach spaces. We also give a variant of Pisier's factorization through Lorentz spaces of factorable (q,p)(q,p)-summing polynomials from C(K)C(K)-spaces. Finally, we show a coincidence result for (q,p)(q,p)-concave polynomials.