On the chaoticity of some tensor product weighted backward shift operators acting on some tensor product Fock-Bargmann spaces

In Advances in Mathematical Physics (2011) we showed that the weighted shift $z^{p}\frac{d^{p+1}}{dz^{p+1}}$ $(p=0, 1, 2, ...)$ acting on classical Bargmann space $\mathbb{B}_{p}$ is chaotic operator. In Journal of Mathematical physics (2014), we constructed an chaotic weighted shift $\mathbb{M}^{*^{p}}\mathbb{M}^{p+1}$ $(p=0, 1, 2, ...)$ on some lattice Fock-Bargmann $\mathbb{E}_{p}^α$ generated by the orthonormal basis $e_{m}^{(α,p)}(z) = e_{m}^α ; m=p, p+1, ...$ where $e_{m}^α(z) = (\frac{2ν}π)^{1/4}e^{\fracν{2}z^{2}}e^{-\frac{π^{2}}ν(m +α)^{2} +2iπ(m +α)z}; m \in \mathbb{N}$ with $ν, α$ are real numbers; $ν> 0$, $\mathbb{M}$ is an weighted shift and $\mathbb{M^{*}}$ is the adjoint of the $\mathbb{M}$. In this paper we study the chaoticity of tensor product $\mathbb{M}^{*^{p}}\mathbb{M}^{p+1}\otimes z^{p}\frac{d^{p}}{dz^{p+1}}$ $(p=0, 1, 2, ...)$ acting on $\mathbb{E}_{p}^α\otimes \mathbb{B}_{p}$.

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