Jessen’s type inequality and exponential convexity for positive C0-semigroups

In this paper a Jessen’s type inequality for normalized positive C 0 -semigroups is obtained. An adjoint of Jessen’s type inequality has also been derived for the corresponding adjoint semigroup, which does not give the analogous results but the behavior is still interesting. Moreover, it is followed by some results regarding positive definiteness and exponential convexity of complex structures involving operators from a semigroup.