Abstract
As we know, B.Sz-Nagy and C.Foins 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 πk spaces. Only a few results have been obtained until today; in particular, the spectral theory of contractions on πk 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, establish the triangle model of contractions on πk spaces and furthermore, apply the triangle model to the study of spectral theory of contractions on πk spaces, which is essential to the harmonic analysis of operators on πk spaces.
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