Functions from the Schoenberg class $\mathscr T$ act in the cone of dissipative elements of a Banach algebra. II

The functional calculus of several commuting dissipative elements of a complex Banach algebra with identity, first introduced in the preceding work by the author, is developed. Uniqueness, continuity, and stability theorems, composite function theorems, and a formula for the resolvent are established. Applications to the theory of sectorial operators in Hilbert space are given.