# IJPAM: Volume 22, No. 1 (2005)

ON REDUCIBILITY OF ADJOINT SEMIGROUPS OF
POSITIVE OPERATORS ON A NORMED RIESZ SPACE

Ömer Gök
Department of Mathematics
Faculty of Arts and Sciences
Yildiz Technical University
Davutpasa Campus
Istanbul, 34210, TURKEY
e-mail: gok@yildiz.edu.tr

Abstract.We prove several results on the existence of invariant closed ideals for adjoint semigroups of positive operators on a normed Riesz space (of dimension greater than 1). If is a multiplicative semigroup of positive operators on a such space that are quasinilpotent at an atom, then adjoint semigroup has a non-trivial invariant closed ideal. Furthermore, if is a non-zero positive operator such that adjoint of , , is quasinilpotent at an atom and if is a multiplicative semigroup of positive operators such that for all , then adjoint semigroup and adjoint have a common non-trivial invariant closed ideal.