Abstract:

For A,B ∈ L(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 δA,B
|Cp (where p 1) have the same numerical range
and are equal to W0(A) − W0(B) (where Cp is the Banach space of the p-Schatten class
operators on H).