## Dilations of Hilbert space operators: (general theory) |

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### Contents

Introduction | 5 |

Minimality and uniqueness of dilations | 13 |

General existence theorems | 23 |

Copyright | |

2 other sections not shown

### Common terms and phrases

a e Sf adjoints approximate identity Banach algebra boundedness condition C*-algebra completes the proof Consequently continuous involution cp is positive define definite operator function definite weakly positive denoted dense dilation space dilation theorems family of operators following conditions following theorem formula functions on groups Hence Hilbert space implies inequality isometric Lemma Let Sf lifting map linear map linear operator linear space map cp matrix minimal dilation n-positive Naimark Neumann algebra norm Notice operators which intertwine orthogonal projection orthogonal sum positive definite function positive definite operator positive functional positive operator prove the following quasi-similarity representation of Sf Schur's lemma Section semi-group of operators semi-group Sf semi-spectral measure space H spectral dilation spectral measure star algebras strong operator topology subspace Suppose symmetric symmetric algebra Sz.-Nagy trivial null space unique unit unitarily unitary isomorphism unitary representation weak operator topology weakly positive definite Wik(X