On Finite Systems of Linear Operators Whose Norms May Be Used to Approximate Their Spectral Radii Simultaneously

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.