An oscillator and virasoro-like operators of c=-2

We define an inverse of the annihilation operator of an oscillator which sa tisfies the Cuntz relations. That enables us to construct Virasoro-like gen erators from an oscillator as a quantum analogue of centerless Virasoro gen erators in a complex plane. The commutators between the generators have a c entral term in operator form, and the trace of this term over the states an nihilated by the generators gives the central term of c = -2. We obtain a s imilar Virasoro-like algebra by modifying the centerless Virasoro generator s on a unit circle by using exponential phase operators which are operator versions of exponential functions. Finally, we discuss extensions and physi cal applications.