## Linear Operators: Spectral theory |

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Page 1776

Q.E.D. 7 CoRollary. Hilbert space is weakly complete and a subset is weakly

3.28, and II.3.29. Q.E.D. 8 DEFINITION. A set A C S) is called an 1776 APPENDix.

Q.E.D. 7 CoRollary. Hilbert space is weakly complete and a subset is weakly

**sequentially compact**if and only if it is bounded. PRoof. This follows from 6, II.3.28, and II.3.29. Q.E.D. 8 DEFINITION. A set A C S) is called an 1776 APPENDix.

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero