Author/Authors :
Cigler، نويسنده , , Grega and Drnov?ek، نويسنده , , Roman and Kokol-Bukov?ek، نويسنده , , Damjana and Omladi?، نويسنده , , Matja? and Laffey، نويسنده , , Thomas J. and Radjavi، نويسنده , , Heydar and Rosenthal، نويسنده , , Peter، نويسنده ,
Abstract :
T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.
