# Hermitian and Positive <i>C</i>-Semigroups on Banach Spacest

### Yuan-Chuan Li

National Central University, Chung-Li, Taiwan### Sen-Yen M. Shaw

National Central University, Chung-Li, Taiwan

## Abstract

Two classes of operator families, namely *n*-times integrated *C*-semigroups of hermitian and positive operators on Banach spaces, are studied. By using Gelfand transform and a theorem of Sinclair, we prove some interesting special properties of such *C*-semigroups. For instances, every hermitian nondegenerate *n*-times integrated C-semigroup on a reflexive space is the *n*-times integral of some hermitian *C*-semigroup with a densely defined generator; an exponentially bounded *C*-semigroup on *Lp*(*μ*) (1 < *p* < ∞) dominates *C* (a positive injective operator) if and only if its generator *A* is bounded, positive , and commutes with *C*; when *C* has dense range, the latter assertion is also true on *Lp*(*μ*) and _C_0(Ω).

## Cite this article

Yuan-Chuan Li, Sen-Yen M. Shaw, Hermitian and Positive <i>C</i>-Semigroups on Banach Spacest. Publ. Res. Inst. Math. Sci. 31 (1995), no. 4, pp. 625–644

DOI 10.2977/PRIMS/1195163918