缺项算子矩阵的补问题

journal6 ›› 2008, Vol. 29 ›› Issue (5): 19-22.

缺项算子矩阵的补问题

出版日期:2008-09-25 发布日期:2012-05-20
作者简介:任芳国(1969-)男,陕西乾县人,陕西师范大学数学与信息科学学院副教授,博士,主要从事算子论研究.
基金资助:
国家自然科学基金资助项目(10571113);陕西师范大学重点基金资助项目(995281)

On the Completion Problems of Operator Partial Matrix

(College of Mathematics and Information Science,Shaanxi Normal University,Xi'an710062,China)

Online:2008-09-25 Published:2012-05-20

摘要/Abstract

摘要：设H和K为复Hiblert空间,给定三元算子对(A,B,C),其中A∈B(H),B∈B(K),C∈B(K,H).对定义在HK上的算子矩阵MX=A CX B,当X取遍B(H,K)中算子时,给出了所有的预解集ρ(MX)之交集的刻画.

关键词： 算子矩阵, 算子补, 预解集, 可控算子

Abstract: Let H and K be complex Hilbert spaces,and the triple (A,B,C) of operators is given,where A∈ B(H),B∈B(K),C∈ B(K，H).For operator matrix A CX B defited on H  K,the intersection of the resolvent set of MX is charecterized when X is taken all operator in B(H，K).

Key words: operator matrix, operator completion, resolvent set, controllable operator

任芳国, 高荣丽. 缺项算子矩阵的补问题[J]. journal6, 2008, 29(5): 19-22.

REN Fang-Guo, GAO Rong-Li. On the Completion Problems of Operator Partial Matrix[J]. journal6, 2008, 29(5): 19-22.