Relations between the Taylor spectrum and the Xia spectrum

Let $\mathbf{ T} = (T_{1},T_{2},...,T_{n})$ be a doubly commuting $n$-tuple of $p$-hyponormal operators $T_{j}$ with unitary operators $U_{j}$ from the polar decompositions $T_{j} = U_{j}|T_{j}| (j=1,...,n)$. Let $\mathbf{ U} = (U_{1},...,U_{n})$ and $A = |T_{1}| \cdots |T_{n}|$. In this paper, we will show relations between the Taylor spectrum $\sigma _{T}(\mathbf{ T})$ and the Xia spectrum $\sigma _{X}(\mathbf{ U},A)$.