## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Results 1-3 of 9

Page 1899

2

40 ) Adjoint space , definition , II . 3 . 7 ( 61 ) of sets . ( See Field of sets )

representation for special spaces , Almost everywhere ( or u - almost everyIV . 15

where ) ...

2

**weakly compact**operator , VI . 4 . 7 - 8 definition , ( 40 ) ( 484 485 ) quotient , (40 ) Adjoint space , definition , II . 3 . 7 ( 61 ) of sets . ( See Field of sets )

representation for special spaces , Almost everywhere ( or u - almost everyIV . 15

where ) ...

Page 1915

4 ( 1188 ) spectrum and resolvent set of , XII . 1 ( 1187 )

definition , VI . 4 . 1 ( 482 ) study of , VI . 4 zero , ( 37 ) Operator topologies , VI . 1

bounded strong , VI . 9 . 9 ( 512 ) bounded weak , V1 . 9 . 7 - 10 ( 512 )

continuous linear ...

4 ( 1188 ) spectrum and resolvent set of , XII . 1 ( 1187 )

**weakly compact**,definition , VI . 4 . 1 ( 482 ) study of , VI . 4 zero , ( 37 ) Operator topologies , VI . 1

bounded strong , VI . 9 . 9 ( 512 ) bounded weak , V1 . 9 . 7 - 10 ( 512 )

continuous linear ...

Page 1923

2 ( 212 ) W Weak Cauchy sequence , criteria for in special spaces , IV . 15

definition , II ... 25 ( 67 ) equivalence of weak and strong convergence in L , IV . 8 .

... 1 – 12 ( 511 - 513 ) weak * topology , ( 462 )

VI . 7 .

2 ( 212 ) W Weak Cauchy sequence , criteria for in special spaces , IV . 15

definition , II ... 25 ( 67 ) equivalence of weak and strong convergence in L , IV . 8 .

... 1 – 12 ( 511 - 513 ) weak * topology , ( 462 )

**Weakly compact**operator , in C ,VI . 7 .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive adjoint operator 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero