  The aim of the present work is to study the Riesz decomposition relative to a
C*-algebra homomorphism T : A --> B. We prove that under some conditions on T,
T-Riesz elements can be decomposed into the sum of almost T-null element and
quasi-nilpotent element. Also the so-called polyno- mial T-Riesz and
generalized T-Riesz decompositions will be discussed.
