Number of homogeneous components of counterexamples to the Dixmier conjecture

Jorge Guccione, Juan Jose Guccione, Christian Valqui

Assume that $P$ and $Q$ are elements of $A_1$ satisfying $[P,Q]=1$. The Dixmier Conjecture for $A_1$ says that they always generate $A_1$. We show that if $P$ is a sum of not mor…