  The proposed third-generation gravitational-wave detectors Einstein Telescope
will have a triangular design that consists of three colocated interferometers.
Summing the strain outputs from the three interferometers will cancel any
gravitational-wave signal and the resultant signal-free stream is known as null
stream. The null stream is in a fixed subspace of the observation space of
Einstein telescope where no gravitational-wave signal can exist. In this paper,
we establish the decomposition of the observation space of Einstein Telescope
into the signal space that contains all possible gravitational-wave signals and
the null space that contains the null stream. We show that the results of
Bayesian parameter estimation and model selection using the strain data in the
signal space are identical to that using the full set of strain data. This
implies that one could use a fraction of the strain data to extract all
information of the source which reduces the memory usage and speeds up the
likelihood evaluation. We also discuss the existence of a fixed null space in
Einstein Telescope allows the unbiased estimation of the noise properties in
the signal-free subspace.
