Abstract:
In the present paper, we introduce and study the concept of norms of derivations, in particular norm estimates of derivations implemented by self-adjoint operators. We show that kδC k = kCX −XCk ≤ 2kCk, for inner derivation while for generalized derivation we establish that kδC,Dk = kCk+kDk, for all C, D, X ∈ B(H). We also estimate that kCk ≤ kCX−XCk ≤ 2kCk and kδC k ≥ 2(kCk 2 + β 2 ) 1 2
