The minimal and maximal operator ideals associated to (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+1)$$\end{document}-tensor norms of Michor’s type

被引：0
作者：
J. A. López Molina
机构：
[1] E. T. S. Ingeniería Agronómica y del Medio Natural,
来源：
Positivity | 2018年 / 22卷 / 4期
关键词：
-fold tensor products; -nuclear and ; -integral ; -linear operators; Ultraproducts; Primary 46M05; 46A32;
D O I：
10.1007/s11117-018-0563-8
中图分类号：
学科分类号：
摘要：
We study an (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+1)$$\end{document}-tensor norm αrC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^C_{\mathbf {r}}$$\end{document} extending to (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n+1)$$\end{document}-fold tensor products a tensor norm defined by Michor when n=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=1$$\end{document} by convexification of a certain s-norm. We characterize the maps of the minimal and the maximal multilinear operator ideals related to αrC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^C_{\mathbf {r}}$$\end{document} in the sense of Defant, Floret and Hunfeld.
引用
收藏
页码：1109 / 1142
页数：33
相关论文
共 15 条
[1]  
Floret K(1997)Natural norms on symmetric tensor products of normed spaces Note Mat. 17 153-188
[2]  
Floret K(2001)Ultrastability of ideals of homogeneous polynomials and multilinear mappings on Banach spaces Proc. Am. Math. Soc. 130 1425-1435
[3]  
Hunfeld S(1980)Ultraproducts in Banach space theory J. Reine Angew. Math. 313 72-104
[4]  
Heinrich S(2007)Multilinear operator ideals associated to Saphar type Positivity 11 95-117
[5]  
López Molina JA(2012)-tensor norms Glasg. Math. J. 54 665-692
[6]  
López Molina JA(2006)-tensor norms of Lapresté’s type Bull. Braz. Math. Soc. 37 191-216
[7]  
López Molina JA(1949)Ultraproduts of real interpolation spaces between Trans. Am. Math. Soc. 65 279-330
[8]  
Puerta ME(1950)-spaces Trans. Am. Math. Soc. 69 142-160
[9]  
Rivera MJ(1932)The representation of abstract measure functions C. R. Acad. Sci. Paris 194 946-948
[10]  
Maharam D(1990)Decompositions of measure algebras and spaces J. Sov. Math. 48 674-681
12