摘要
设H1,H2,H3为无穷维复可分Hilbert空间,对给定关系A ∈BCR(H1),B∈ B CR(H2),C ∈ BCR(H3),记 MD,E,F:=(A D E 0 B F 0 0 C),其中 D ∈ BR(H2,H1),E ∈ B(H3,H1),F∈ BR(H3,H2).得到了对任意 D ∈ B(H2,H1),E ∈ B(H3,H1),F ∈ B(H3,H2)和 D∈ BR(H2,H1),E∈B(H3,H1),F∈B(H3,H2),关系矩阵 MD,E,F 都有闭值域的充分必要条件,并进一步刻画了两类3×3上三角关系矩阵的可能闭值域谱.
Abstract
Let H1,H2 and H3 be complex separable infinite-dimensional Hilbert spaces.Given the relations A∈BCR(H1),B∈BCR(H2)and C∈BCR(H3),MD,E,F:=(A D E 0 B F 0 0 C)is defined,where D ∈ BR(H2,H1),E∈ BR(H3,H1)and F ∈ BR(H3,H2)are bounded relations.Some neces-sary and sufficient conditions are presented under which the range of MD.E,F is closed for any bound-ed operator D∈ B(H2,H1),E∈ B(H3,H1),F∈ B(H3,H2)and relation D ∈ BR(H2,H1),E∈ B(H3,H1),F∈ B(H3,H2).And two classes of possible closed range spectrums of 3 X 3 upper trian-gular relation matrices are furtherly characterized.
基金项目
内蒙古自然科学基金项目(2022LHMS01003)
内蒙古高等学校青年科技英才项目(NJYT22029)
数学一流学科科研专项(YLXKZX-NSD-011)
内蒙古师范大学基本科研业务费专项(2022JBBJ009)
内蒙古师范大学数学一流拔尖培育学科建设项目(2024YLKY07)
无穷维哈密顿系统及其算法应用教育部重点实验室开放课题(2023KFZD01)
无穷维哈密顿系统及其算法应用教育部重点实验室开放课题(2023KFZD02)
维普
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