$H^{∞}$ functional calculus for sectorial and bisectorial operators
We give a concise exposition of the basic theory of H∞ functional calculus for N -tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator f(T1, . . . , TN ) when f is an R-bounded operator-valued holomorphic function.