چکیده
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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.
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