The numerical range of elementary operators II Original Research Article

For A,Bset membership, variantL(H) (the algebra of all bounded linear operators on the Hilbert space H), it is proved that: (i) the generalized derivation δA,B is convexoid if and only if A and B are convexoid; (ii) the operators δA,B and image (where pgreater-or-equal, slanted1) have the same numerical range and are equal to W0(A)−W0(B) (where image is the Banach space of the p-Schatten class operators on H).