  A Lindblad master equation for a harmonic oscillator, which describes the
dynamics of an open system, is formally solved. The solution yields the
spectral resolution of the Liouvillian, that is, all eigenvalues and
eigenprojections are obtained. This spectral resolution is discussed in depth
in the context of the biorthogonal system and the rigged Hilbert space, and the
contribution of each eigenprojection to expectation values of physical
quantities is revealed. We also construct the ladder operators of the
Liouvillian, which clarify the structure of the spectral resolution.
