## Linear Operators: Spectral theory |

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Page 1913

6 ( 416 ) Mean ergodic theorem , ( 728 – 729 ) continuous case in B - space , VII1

. 7 . 1 - 3 ( 687 - 689 ) in L ... 11 - 12 ( 106 ) space of ( totally ) , criterion for

completeness , III . 6 . 5 ( 146 ) ... 18 ( 143 ) as a

. 9 .

6 ( 416 ) Mean ergodic theorem , ( 728 – 729 ) continuous case in B - space , VII1

. 7 . 1 - 3 ( 687 - 689 ) in L ... 11 - 12 ( 106 ) space of ( totally ) , criterion for

completeness , III . 6 . 5 ( 146 ) ... 18 ( 143 ) as a

**metric space**, III . 7 . 1 ( 158 ) , III. 9 .

Page 1914

( See also Functional ) Multiplicity of eigenvalues , X . 4 ( 907 ) in special spaces ,

IV . ... 14 ( 563 ) in Hilbert space X . 1 ( 887 ) real and imaginary parts of , X . 4 (

906 ) Normal structure , definition , V . 11 . 14 ( 459 ) ... 1 ( 15 )

.

( See also Functional ) Multiplicity of eigenvalues , X . 4 ( 907 ) in special spaces ,

IV . ... 14 ( 563 ) in Hilbert space X . 1 ( 887 ) real and imaginary parts of , X . 4 (

906 ) Normal structure , definition , V . 11 . 14 ( 459 ) ... 1 ( 15 )

**metric space**, 1 . 6.

Page 1921

3 ( 427 ) functional or I topology , V . 3 . 2 ( 419 ) study of , V . 3 linear

See Operator topology )

3 ( 427 ) functional or I topology , V . 3 . 2 ( 419 ) study of , V . 3 linear

**spaces**. (See Operator topology )

**metric**, definition , 1 . 6 . 1 ( 18 )**metric**or strong , in a B -**space**, ( 419 ) study of , 1 . 6 norm or strong , in a normed . linear**space**, II . 3 .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive 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 singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero