Factorizing Kernel Operators

被引:0
作者
O. Galdames. Bravo
E. A. Sánchez. Pérez
机构
[1] Universidad Politécnica de Valencia,Instituto Universitario de Matemática Pura y Aplicada
来源
Integral Equations and Operator Theory | 2013年 / 75卷
关键词
Primary 46E30; Secondary 47B38; 46B42; 47B34; Banach function space; Köthe duality; -th power factorable operator; factorization; kernel operator;
D O I
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中图分类号
学科分类号
摘要
Consider an operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T: X(\mu) \rightarrow Y(\mu)}$$\end{document} between Banach function spaces having adequate order continuity and Fatou properties. Assume that T can be factorized through a Banach space as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T = S \circ R}$$\end{document} , where R and the adjoint of S are p-th power and q-th power factorable, respectively. Then a canonical factorization scheme can be given for T. We show that it provides a tool for analyzing T that becomes specially useful for the case of kernel operators. In particular, we show that this square factorization scheme for T is equivalent to some inequalities for the bilinear form defined by T. Kernel operators are studied from this point of view.
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页码:13 / 29
页数:16
相关论文
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