# Riesz Decomposition Relative to C*-Algebra Homomorphisms

## TL;DR

This paper investigates the Riesz decomposition relative to C*-algebra homomorphisms, establishing conditions under which T-Riesz elements can be decomposed into almost T-null and quasi-nilpotent parts, and discusses polynomial and generalized decompositions.

## Contribution

It introduces new conditions for T-Riesz element decomposition relative to C*-algebra homomorphisms and explores polynomial and generalized decompositions.

## Key findings

- T-Riesz elements can be decomposed into almost T-null and quasi-nilpotent elements under certain conditions
- Discussion of polynomial T-Riesz and generalized T-Riesz decompositions
- Provides theoretical framework for Riesz decomposition in C*-algebra homomorphisms

## Abstract

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.