解剖算子及其一致有界定理  

Dissecting Operator and Its Uniform Boundedness Principle

作　　者：刘铁[1] 郑亮[2] 

机构地区：[1]安康学院数学系,陕西安康725000 [2]哈尔滨工业大学深圳研究生院,深圳518055

出　　处：《重庆理工大学学报（自然科学）》2012年第3期126-129,共4页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(10702017)

摘　　要：将泛函分析基本原理拓展到包括一些非线性映射的更大映射类。讨论了实数空间解剖算子的性质,得出其连续性和原点邻域内的零点具有唯一性,非平凡赋范线性空间到线性空间的非线性解剖算子的势不小于线性算子的势。证明了解剖算子下的一致有界定理。The study on dissecting operators is aimed at expanding functional analysis principle to the more extensive mapping class including some nonlinear mapping. Some properties of dissecting operators on the space of real numbers are discussed. Firstly, uniqueness is obtained on its continuity and null point in neighborhood. Then, we prove that cardinality of nonlinear dissecting operator on non- trivial norm linear space to nontrivial linear space is not less than the cardinality of linear operator, which proves the uniform boundedness principle on dissecting operator.

关 键 词：线性空间 赋范空间 解剖算子 势 一致有界原理 

分 类 号：O177.2[理学—数学]