## An Introduction to Linear Transformations in Hilbert Space, Volume 4The description for this book, An Introduction to Linear Transformations in Hilbert Space. (AM-4), will be forthcoming. |

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### Contents

Preface | |

REALIZATIONS OF HILBERT SPACE | 22 |

ADDITIVE AND CLOSED TRANSFORMATIONS | 31 |

WEAK CONVERGENCE | 45 |

PROJECTIONS AND ISOMETRY | 51 |

RESOLUTIONS OF THE IDENTITY | 64 |

BOUNDED SELFADJOINT AND UNITARY | 81 |

CANONICAL RESOLUTION AND INTEGRAL | 95 |

SYMMETRIC OPERATORS | 110 |

REFERENCES TO FURTHER DEVELOPMENTS | 122 |

REFERENCES TO APPLICATIONS | 130 |

### Other editions - View all

An Introduction to Linear Transformations in Hilbert Space. (AM-4) Francis Joseph Murray Limited preview - 2016 |

### Common terms and phrases

Banach space bounded Cayley transform Chapter VII shows closed isometric closed symmetric closure commutes with H complete orthonormal set consider continuous corollary to Theorem defined DEFINITION dense discussion domain of H equation equivalent exists f and g final set finite dimensional Furthermore given H is closed H+i)f Hf,f Hf,g Hilbert space identity implies f improper integral infinite initial set integral representation interval isometric transformation LEJWA LENMA Let f let g Let H limit linear functionals linear transformation linearly independent maximal symmetric Neumann normal operator obtain pair partially isometric Postulate projection with range proof of Lemma properties range of F readily seen result rings of operators self-adjoint operator self-adjoint transformation sequence f sequence of elements set of elements sphere statement symmetric extension SYMMETRIC OPERATORS Theorem II Theorem VII tion UNITARY OPERATOR unitary transformation VIII weakly convergent zero