On Finite Systems of Linear Operators Whose Norms May Be Used to Approximate Their Spectral Radii Simultaneously |
Received:October 04, 1983 |
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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. |
Citation: |
DOI:10.3770/j.issn:1000-341X.1986.03.029 |
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