The operator equation $\lambda M_{\overline z} X = X M_{z^k}$, for $k \geq 2, $ $\lambda \in \mathbb{C}$, is completely solved. Further, some algebraic and spectral properties of the solutions of the equation are discussed.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n4.6}, url = {http://global-sci.org/intro/article_detail/ata/4678.html} }