An element $z$ of a Banach algebra $A$ is called a topological divisor of zero if there exists a sequence $x_1$, $x_2$, $x_3$, ... of elements of $A$ such that the sequence $zx_n$ converges to the zero element, but the sequence $x_n$ does not converge to the zero element.
However, I am not able to apply this definition in the paper mentioned above. Is there any other definitions of topological divisor of zero? Please explain me about this term so that I can understand why author of the paper has used this term?
Please help and thanks for all.