Dissipative operators on Banach spaces

A bounded linear operator T on a Banach space is said to be dissipative if ‖etT‖?1 for all t?0. We show that if T is a dissipative operator on a Banach space, then:

(a)

.

(b)

If σ(T)∩iR is contained in −iπ/2,iπ/2], then