Decomposition results from Chapter 5 and model results from Chapter 6 will be combined to yield further pattern and decomposition results. First we shall combine Nagy-Foiaş-Langer decomposition for contractions and the Durszt model for completely nonunitary contractions to get a pattern for general contractions, which can be viewed as a kind of ultimate extension of patterns for contractions. Next we shall combine such a pattern for general contractions and Nagy-Foiaş-Langer decomposition again to get Foguel decomposition, which says that every contraction can be decomposed into a direct sum of a weakly stable contraction and a unitary operator.
KeywordsUnitary Operator Invariant Subspace Direct Summand Weak Stability General Contraction
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