The Spectral Theory of Contractions on II, Spaces

As we know, B.Sz-Nagy and C.Foiss studied systematically contractions on Hilbert spaces and developed the harmonic analysis theory of operators on Hilbert spaces. Since 1950s, people paid great attention to the study of contractions on .. spaces. Only a few results have been obtained until today; in particular, the spectral theory of contractions on .. Spaces and corresponding harmonic analysis theory have left still unexplored. This paper, as a continuation. of [1], [2], [6], in which the authors after discussing some problems such as the negative invariant subspaces and unitary dilations of contractions on complete spaces with indefinite metrics, estab lish the triangle model of contractions on .. spaces and furthermore, apply the triangle model to the study of spectral theory of contractions on .. spaces, which is essential to the harmonic analysis of operators on .. spaces.