J-orthostochastic matrices of size 3 × 3 and numerical ranges of Krein space operators

A result of Au-Yeung and Poon on 3 × 3 orthostochastic matrices is extended to analogous operators arising in the context of indefinite inner product spaces. This result is used to study the numerical range of certain operators on a three-dimensional Krein space. In particular, the convexity and the boundary of the set are investigated.