## Spectral theory of operators in Hilbert space |

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### Contents

Spectral Representation | ii |

Norm and Inner Product | 31 |

Hilbert Space | 64 |

Copyright | |

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### Common terms and phrases

apply approximated assigned assume atth bounded operators bounded support Cauchy sequence ceasp Chapter chsu Clearly closeable closure complete space components convergence coordinate system corollary defined denote dense differential operators dimension domain eigen eigenspace eigenvalue eigenvectors equation evidently fact finite number finite-dimensional follows formally adjoint formally self-adjoint formula func function space functions 0(s given hence Hermitean operator Hilbert space holds Holmgren norm ideal elements ideal functions identity implies inequality infinite inner product space integral operator introduce kernel k(s,s Lemma linear combination linear space maximum norm measure function mrof non-negative notion open interval operator f(A orthogonal piecewise constant piecewise continuous functions polynomials projection theorem projector prove quadratic form relation respect rtoaterop Section self-adjoint operator shiq spectral representation spectrum statement step function strict adjoint strictly self-adjoint subspace Suppose theory thTw tion triangle inequality unit form values vanishes variable vector H