On $q$-normal operators and quantum complex plane

Abstract

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 $q$-moment problem, positive elements and sums of squares.

References in corpus (1)

• Maximal quadratic modules on *-rings

Cited by in corpus (4)

• A Real Nullstellensatz for Free Modules
• Function algebras on a 2-dimensional quantum complex plane
• Function algebras on the n-dimensional quantum complex space
• Induced quadratic modules in $\ast$-algebras