\begin{definition}[Definition:Convergent Product/Normed Algebra]
Let $\mathbb K$ be a division ring with norm $\norm {\,\cdot\,}_{\mathbb K}$.
Let $\struct {A, \norm {\,\cdot\,} }$ be an associative normed unital algebra over $\mathbb K$.
Let $\sequence {a_n}$ be a sequence in $A$.
\end{definition}