LAUSR

In the present paper, we are mainly concerned with the existence of a Riesz basis related to the Gribov operator $$\begin{aligned} A^{*2}A^2+\varepsilon (A^* A + A^* (A + A^* )A), \end{aligned}$$A∗2A2+ε(A∗A+A∗(A+A∗)A),where $$\varepsilon \in \mathbb {C}$$ε∈C; while A is the annihilation operator and $$A^*$$A∗ is the creation operator verifying $$[A, A^*] = I.$$[A,A∗]=I. Through a specific growing inequality, we extend this problem to a theoretical one and we study the invariance of the closure, the comportment of the spectrum as well as the existence of Riesz basis of generalized eigenvectors.