Définition 4

Let A be a normed algebra, let $x$ be an element of A. Let us denote by $\boldsymbol{\gamma }_x$ and $\boldsymbol{\delta }_x$ the mappings $y\mapsto xy$ and $y\mapsto yx$ of A into A. We say that $x$ is a topological zero divisor on the left (resp. right) if $\boldsymbol{\gamma }_x($resp. $\boldsymbol{\delta }_x)$ is not a homeomorphism of A onto $\boldsymbol{\gamma }_x(A)$ (resp. onto $\boldsymbol{\delta }_x(A)$).