APP下载

一类算子的无穷矩阵族的刻划

2019-09-10顾娟单净姜文彪赵淑莹杜广环王宏久

赤峰学院学报·自然科学版 2019年11期

顾娟 单净 姜文彪 赵淑莹 杜广环 王宏久

摘 要:研究了一類更广泛的包含全部线性算子、齐性算子和某些非线性算子在内的无穷矩阵变换,得到向量值序列赋值收敛的等价条件,进而刻划无穷矩阵族(c0(X),l∞(I,Y))的特征,该结果是非线性无穷矩阵变换理论有益的补充.

关键词:无穷矩阵变换;一致收敛;制动空间

中图分类号:O177.3  文献标识码:A  文章编号:1673-260X(2019)11-0006-02

参考文献:

〔1〕Maddox I. J. Infinite Matrices of Operators [J]. Spinger-Verlag Berlin Heidelberg New York. 1980:51~58.

〔2〕Li R., Swartz C. A nonlinear Schur theorem[J]. Acta Sci. Math, 1993, 58: 497-508.

〔3〕Swartz C. Infinite Matrices and the Gliding Hamp. Singapore. World Scientifie Publ. 1996:42~46.

〔4〕Li R, Kang S, and Swartz C. Operator Matrices on Topological Vector Spaces [J]. Math. Anal. Appl. 2002, 274(2): 645~658.

〔5〕Guo H, Li R, Wu J. Matrix Transformations of Lq(X) to Lp(X) [J]. Appl. Math. J. Chinese Univ.2012, 27(1): 78~86.

〔6〕Gu J. Infinite Matrix Transformation of a Class of Operator[C]//Advanced Materials Research. Trans Tech Publications, 2012, 542: 1371~1375.

〔7〕Eren R S. Infinite Matrices and Some Matrix Transformations [J]. Filomat, 2016, 30(3): 815 ~ 822.

〔8〕Li R, Zhong S, Li L. Demi-linear analysis I-basic principles[J]. Journal of the Korean  Mathematical Society. 2009, 46(3): 643~656.

〔9〕Khaleelulla S M. Counterexamples in Topological Vector Spaces[M]. Springer-Verlag, Heidelberg, 2006.

〔10〕Li R, Wang J. Invariants in abstract mapping pairs[J]. Journal of the Australian Mathematical Society, 2004, 76(3): 369~382.