Integral representation formula for generalized normal derivations
Danko R. Jocić · Proceedings of the American Mathematical Society · 1999
For generalized normal derivations, acting on the space of all bounded Hilbert space operators, the following integral representation formulas hold: f ( A ) X − X f ( B ) = ∫ σ ( A ) ∫ σ ( B ) f ( z ) − f ( w ) z − w E ( d z ) ( A X − X B ) F ( d w ) , \begin{equation} f(A)X-Xf(B)=\int _{ \sigma (A)}\int _{\sigma (B)}\frac {f(z)-f(w)}{z-w}\,E(dz)\,(AX-XB)F(dw), \end{equation} and ‖ f ( A ) X − X f ( B ) ‖ 2 2 a m p ; a m p ; = ∫ σ ( A )