On the equation $\mathbf{h}x - x \mathbf{k}=c$ in Banach algebra $A$ with Hermitian coefficients $\mathbf{h},\mathbf{k}$

This work investigates the problem of solvability on the equation $\mathbf{h}x - x\mathbf{k}=c$ with Hermitian coefficients $\mathbf{h},\mathbf{k}$ of weak complete Banach algebra $A$. In the article (theorem 1) the criterion of solvability of equation $\mathbf{h}x-x\mathbf{k}=c$ is proved, which implies (theorem 2) the following algebraic criterion of solvability. For solvability in $A$ the equation $\mathbf{h}x-x\mathbf{k}=c$ the similarity of matrixes $\left(
\begin {array}{cc}\mathbf{h}, & 0 \\ 0, &\mathbf{k} \end {array}
\right)$ and $\left(
\begin {array}{cc}\mathbf{h}, & 0 \\ c, &\mathbf{k} \end {array}
\right)$ is necessary and sufficient.