ON SOME CLASSES OF OPERATORS DETERMINED BY THE STRUCTURE OF THEIR MEMORY
ON SOME CLASSES OF OPERATORS DETERMINED BY THE STRUCTURE OF THEIR MEMORY
复制标题
关于由内存结构决定的某些运算符类别
DOI：
10.1017/s0013091500000821
复制
发表时间：
2002
影响因子：
0.7
通讯作者：
E. Stepanov
中科院分区：
文献类型：
--
作者：
M. E. Drakhlin;A. Ponosov;E. Stepanov
摘要引入了两类非线性算子，推广了理想函数空间之间的局部算子的概念。第一类，称为原子，包含特别是所有的线性位移，而第二个，称为coatomic，包含所有的伴随前，特别是条件期望。这两个类都包含局部（特别是Nemytski\v{\i}）运算符，并且相对于运算符的合成是封闭的。研究了向量值函数的Lebesgue空间中引入类算子的基本性质。结果表明，这两类算子继承了Nemytski\v{\i}算子的测度非紧性和弱退化性，但在作用性、连续性和有界性方面存在着不同的关系，收敛性也不同.代表这两个类的运营商的结果提供。引入类的定义以及它们的性质的证明是基于一个纯粹的测量理论的概念的记忆的运营商，本文也介绍了。AMS 2000数学科目分类：小学47 B38; 47 A67; 34 K 05
Abstract Two classes of nonlinear operators generalizing the notion of a local operator between ideal function spaces are introduced. The first class, called atomic, contains in particular all the linear shifts, while the second one, called coatomic, contains all the adjoints to former, and, in particular, the conditional expectations. Both classes include local (in particular, Nemytski\v{\i}) operators and are closed with respect to compositions of operators. Basic properties of operators of introduced classes in the Lebesgue spaces of vector-valued functions are studied. It is shown that both classes inherit from Nemytski\v{\i} operators the properties of non-compactness in measure and weak degeneracy, while having different relationships of acting, continuity and boundedness, as well as different convergence properties. Representation results for the operators of both classes are provided. The definitions of the introduced classes as well as the proofs of their properties are based on a purely measure theoretic notion of memory of an operator, also introduced in this paper. AMS 2000 Mathematics subject classification: Primary 47B38; 47A67; 34K05