【摘要】 <正>本文证明了Banach空间上任意有限个两两可换的线性算子可同时(即在与原空间范数等价的同一范数下)用其范数任意逼近于各自的谱半径。在有限维情形,更进一步推广上述结果到可同时化为上(或下)三角阵的算子族。更多还原

【Abstract】 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.更多还原