International Journal of Mathematics and Mathematical Sciences 
Volume 14 (1991), Issue 1, Pages 83-92
doi:10.1155/S016117129100008X

An absolute continuity for positive operators on Banach lattices

W. Feldman,1 C. Piston,1 and Calvin E. Piston2

 1Department of Mathematics, University of Arkansas, Fayetteville 72701, Arkansas, USA
2Department of Mathematics, John Brown University, Siloam Springs 72761, Arkansas, USA
Received 19 July 1990

Abstract

For positive operators on a Banach lattice, absolute contnuity conditions are considered. An operator absolutely continuous with respect to T is compared to sums of compositions of T together with orthomorphisms or in special cases projections. Consequences For compact operators on functions spaces C(X) are considered.