The spectrum of contractive operators on \(\pi _ k\) (Q5899723)

The author observes a J-contraction T on a Pontryagin space \(\Pi_ k\) with maximal negative subspace of dimension k. It is shown that the spectrum of T outside the closed unit disc consists of a finite number of isolated eigenvalues, each of which has finite multiplicity. The J- contraction T always admits a J-unitary dilation U on a Pontryagin space \(\Pi_ k\oplus H\) with a Hilbert space H. It is shown that on the unit circle T and U have the same set of eigenvalues.