游兆永,刘忠贵.若干个线性算子的范数同时逼近于其谱半径之可能性[J].数学研究及应用,1986,6(3):99~102
若干个线性算子的范数同时逼近于其谱半径之可能性
On Finite Systems of Linear Operators Whose Norms May Be Used to Approximate Their Spectral Radii Simultaneously
投稿时间:1983-10-04  
DOI:10.3770/j.issn:1000-341X.1986.03.029
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游兆永 西安交通大学数学系 
刘忠贵 西安交通大学数学系 
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      In this paper it is proved that a family of linear operatots on' a Banach space which are commutative with each other may approxi-mate their spectral radii with their respective norms simultaneously (i.e., under a common space norm equivalent to the original one ) . For the finite dimension case it is further shown that the above result can be extended to a family of operators which can be reduced simultaneously to upper (or lower ) triangular matrices.
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