山东科学2012，Vol.25Issue(1)：1-4,4.
分块矩阵的块数值值域等于谱的条件
The condition of the block numerical range of a block operator matrix equal to its spectrum
摘要
Abstract
Let Hi（i= 1,2,..., n） be unitary space. Let A be a linear operator on H = H1 H2 ... Hn with block matrix expression （lAst n≤ dim Hi 〈 = ）. This paper presents a necessary and sufficient condition of the block numerical range of matrix .4 equal to its spectrum ： a set of complex numbers λ1,λ2,…,λ m, （ m≤ n） exist and Ai, = μiⅠ（ i = t ,2,..., n）. Moreover, the set of all μ is equal to { λ1,λ2,…,λm} , and can be transformed into an upper triangular block matrix by some elementary row operations and the corre.cnnnding elementary column,operations关键词
块数值值域/谱/分块算子矩阵Key words
block numerical range： spectrum/block operator matrix分类
数理科学引用本文复制引用
翟发辉,韩杰..分块矩阵的块数值值域等于谱的条件[J].山东科学,2012,25(1):1-4,4.基金项目
山东省高等学校科技计划项目 （）
