## Linear Operators: Spectral theory |

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Page 1900

( See also Hamel base ) in a

260 ) definition , II . 4 . 7 ( 71 ) properties , II . 4 . 8 - 12 ( 71 ) remarks on , ( 93 - 94

) in a linear space . ( See Hamel base ) orthogonal and orthonormal bases in ...

( See also Hamel base ) in a

**B**-**space**, criterion for compactness with , IV . 5 . 5 (260 ) definition , II . 4 . 7 ( 71 ) properties , II . 4 . 8 - 12 ( 71 ) remarks on , ( 93 - 94

) in a linear space . ( See Hamel base ) orthogonal and orthonormal bases in ...

Page 1914

1 ( 15 ) metric space , 1 . 6 . 3 ( 19 ) properties , 1 . 5 . 24 ( 15 - 17 ) regular space

with countable base , ( 24 ) Normed ( normed linear space ) . ( See also

) definition , II . 3 . 1 ( 59 ) study of , II . 3 Nowhere dense , 1 . 6 . 11 ( 21 ) Null ...

1 ( 15 ) metric space , 1 . 6 . 3 ( 19 ) properties , 1 . 5 . 24 ( 15 - 17 ) regular space

with countable base , ( 24 ) Normed ( normed linear space ) . ( See also

**B**-**space**) definition , II . 3 . 1 ( 59 ) study of , II . 3 Nowhere dense , 1 . 6 . 11 ( 21 ) Null ...

Page 1921

space , definition , ( 398 ) theorems on representation of Boolean rings and

algebras , 1 . 12 . 1 ( 41 ) , ( 44 ) - Weierstrass theorem , IV . 6 . 16 ( 272 ) complex

case , IV . 6 . 17 ( 274 ) remarks on , ( 383 – 385 ) Strictly convex

space , definition , ( 398 ) theorems on representation of Boolean rings and

algebras , 1 . 12 . 1 ( 41 ) , ( 44 ) - Weierstrass theorem , IV . 6 . 16 ( 272 ) complex

case , IV . 6 . 17 ( 274 ) remarks on , ( 383 – 385 ) Strictly convex

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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additive adjoint operator Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero