## Harmonic analysis of operators on Hilbert space |

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### Contents

CHAPTER | 1 |

Bilateral shifts | 4 |

Contractions Invariant vectors and canonical decomposition | 6 |

Copyright | |

50 other sections not shown

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Harmonic analysis of operators on Hilbert space Béla Szökefalvi-Nagy,Ciprian Foiaş Snippet view - 1970 |

### Common terms and phrases

accretive operator belongs bilateral shift bounded operator boundedly invertible c.n.u. contraction canonical factorization Cayley transform characteristic function class C0 cogenerator coincides concludes the proof condition consequently continuous one parameter contraction of class contractive analytic function convergence corresponding decomposition deduce defect indices defined dense dissipative operators eigenvalue equal exists a contractive fact functional calculus functional model hence it follows Hilbert space holomorphic hyperinvariant implies inequality inner function invariant subspace Lemma Let us consider Let us observe linear matrix maximal accretive minimal function minimal unitary dilation Moreover necessary and sufficient non-trivial obtain obvious orthogonal projection outer function particular proved quasi-similar regular divisor regular factorization relation respectively satisfies scalar multiple scalar valued self-adjoint operator semi-group of contractions sequence spectral measure spectrum subset Sz.-Nagy triangulation unicellular unilateral unit circle unit disc unitarily equivalent unitary constant unitary operator vectors virtue of Proposition weak contraction