  In this article, we prove the following spectral theorem for right linear
normal operators (need not to be bounded) in quaternionic Hilbert spaces: Let
$T$ be an unbounded right quaternionic linear normal operator in a quaternionic
Hilbert space $H$ with domain $\mathcal{D}(T)$, a right linear subspace of $H$
and fix a unit imaginary quaternion, say $m$. Then there exists a Hilbert basis
$\mathcal{N}$ of $H$ and a unique quaternionic spectral measure $F$ on the
$\sigma$- algebra of $\mathbb C_m^{+}$ (upper half plane of the slice complex
plane $\mathbb C_m$) associated to $T$ such that \begin{equation*}
  \left\langle x | Ty \right\rangle = \int\limits_{\sigma_{S}(T) \cap
\mathbb{C}_{m}^{+}}\lambda \ dF_{x,y}(\lambda),\; \text{ for all}\; y \in
\mathcal{D}(T),\ x \in H, \end{equation*} where $F_{x,y}$ is a quaternion
valued measure on the $\sigma$- algebra of $\mathbb{C}_{m}^{+}$, for any
$x,y\in H$ and $\sigma_{S}(T)$ is the spherical spectrum of $T$. Here the
representation of $T$ is established with respect to the Hilbert basis
$\mathcal{N}$.
  To prove this result, we reduce the problem to the complex case and obtain
the result by using the classical result.
