Research Communication | Open Access
Volume 2019 | Communication ID 136
Volume 2019 | Communication ID 136
| Polynomially Riesz elements |
Safae Alaoui Chrifi, Abdelaziz Tajmouati, Abdeslam El Bakkali
Received |
Accepted |
Published |
Jan 29, 2019 |
Feb 26, 2019 |
Mar 01, 2019 |
Abstract: Given two complex unitary Banach algebras $A$ and $B$ and an algebra homomorphism $\mathcal{T}:A\longrightarrow B$ An element $a\inA $ is said to be "polynomially $\mathcal{T}$-Riesz" if there exists a non zero complex polynomial $P$ such that $\mathcal{T}P(a)$ is a quasi-nilpotent element of $B$. Our purpose in this talk is to study polynomially Riesz element relative to an arbitrary Banach algebra homomorphism. Mainly, we present sevral properties of polynomially Riesz elements which leading us to give a decomposition to these elements in $C^{\star}$-algebra.