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

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Page 1378

matrix measure { fus } , i , j = 1 , ... , k of

matrix measure { fus } , i , j = 1 , ... , k of

**Theorem**23 is unique , and Pii Pij , i , j = 1 , ... , k ; Pij = 0 , if i > k or ; > k . Proof . Suppose that 01 , ... , 01 is a determining set for T. Then it is evident from**Theorem**23 ...Page 1379

{ ôij } is the matrix measure of

{ ôij } is the matrix measure of

**Theorem**23 , the values Pis ( e ) are uniquely determined for each e C N. Since 1 is the union of a sequence of neighborhoods of the same type as N , the uniqueness of { u } follows immediately .Page 1904

limits , IV.6.11 ( 268 ) Banach

limits , IV.6.11 ( 268 ) Banach

**theorem**for operators into space of measurable functions , IV.11.2–3 ( 332–333 ) examples of ... ( See also Ergodic**theorems**) in general spaces , VII.3.13 ( 571 ) , VII.3.23 ( 576 ) , VII.5.32 ( 584 ) by ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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