محمدرضا عظیمی

Let $G$ be a second countable locally compact group, $\mathcal{B}$ a Borel $\sigma$-algebra and let $v$ be a Borel measurable weight function on $G$. In this paper, we study the subspace-hypercyclicity of the conditional weighted translation $R_{g, v}(f):= E^{\mathcal{A}}(v f*\delta_g)$ on $L^p(\mathcal{B})$, $1\le p<\infty$, where $\delta_g$ is the unit point mass measure at $g\in G$ and $E^{\mathcal{A}}$ is the conditional expectation operator associated with the $\sigma$-subalgebra $\mathcal{A}$. For an aperiodic element $g\in G$, we give the necessary and sufficient conditions on which $R_{g, v}$ is subspace-hypercyclic for $L^p(\mathcal{A})$ and $L^p(\mathcal{A}_D)$. The subspace-mixing concept for $R_{g, v}$ is also characterized. Furthermore, the subspace-hypercyclicity of the adjoint of $R_{g, v}$ with respect to $L^2(\mathcal{A}g^{-1})$ and other some specific subspaces is studied. Finally, some examples are then given to illustrate the obtained results.