Generalized derivation, SVEP, finite ascent, range closure
Generalized derivation, SVEP, finite ascent, range closure
Let X be an infinite complex Banach space and consider two bounded linear operators A,B ? L(X). Let LA ? L(L(X)) and RB ? L(L(X)) be the left and the right multiplication operators, respectively. The generalized derivation ?A,B ? L(L(X)) is defined by ?A,B(X) = (LA-RB)(X) = AX-XB. In this …