AN EXTREMAL PROPERTY OF CONTRACTION SEMIGROUPS IN BANACH SPACES

摘要

Let the closed operator B generate a (C_0) contraction semigroup T on a complex Banach space X, and let f be a unit vector in X. It is evident that if f is an eigenvector of B corresponding to a purely imaginary eigenvalue, then |< T_tf,x~* >| = |< f, x~* >| for every functional x~* in the dual space X~*.