  We extend elliptical slice sampling, a Markov chain transition kernel
suggested in Murray, Adams and MacKay 2010, to infinite-dimensional separable
Hilbert spaces and discuss its well-definedness. We point to a regularity
requirement, provide an alternative proof of the desirable reversibility
property and show that it induces a positive semi-definite Markov operator.
Crucial within the proof of the formerly mentioned results is the analysis of a
shrinkage Markov chain that may be interesting on its own.
