This paper continues the study
of isometries on indefinite inner product spaces by means of their wandering
subspaces. In the author’s earlier paper of the same title (Pacific J. Math., 81 (1979),
113–130), it was shown that the subspace on which an isometry acts as a shift need
not be regular and that vectors in this subspace need not be recoverable
from their Fourier coefficients by summation. We present here necessary and
sufficient conditions for this situation not to occur, and also show that these
conditions are sufficient (but not necessary) for the isometry to have a Wold
decomposition.
