On $q$-normal operators and quantum complex plane

Jaka Cimpric, Yurii Savchuk, Konrad Schmüdgen

For $q>0$ let $\cA$ denote the unital $\ast$-algebra with generator $x$ and defining relation $x{x}^{\ast }=qx{x}^{\ast }$. Based on this algebra we study $q$-normal operators, the complex $…