Abstract :
Let $T$ be a bounded operator on the Banach space $X$ and $\ph$ be an analytic self-map of the unit disk $\Bbb{D}$. We investigate some operator theoretic properties of bilateral composition operator $C_{\ph, T}: f \ri T \circ f \circ \ph$ on the vector-valued Hardy space $H^p(X)$ for $1 \leq p \leq +\infty$. Compactness and weak compactness of $C_{\ph, T}$ on $H^p(X)$ are characterized and when $p=2$, a concrete formula for its adjoint is given.
