## Linear Operators: Spectral theory |

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Page 1147

COROLLARY : If G is a compact topological group satisfying the second axiom of

countability , and G is not a finite set , then any

G is countable . A

COROLLARY : If G is a compact topological group satisfying the second axiom of

countability , and G is not a finite set , then any

**complete**set of representations ofG is countable . A

**complete**set of representations of a finite group is finite .Page 1297

6 ) D ( T ( ) ) is

the norm of f as an element of H " ( J ) it follows easily that D ( T ( T ) ) is also

two ...

6 ) D ( T ( ) ) is

**complete**in the norm Iflı . Since the two additional terms in 112 arethe norm of f as an element of H " ( J ) it follows easily that D ( T ( T ) ) is also

**complete**under the norm \ | l2 . As It S \ fait follows from Theorem II . 2 . 5 that thetwo ...

Page 1903

3 . 28 ( 68 ) Complement , orthocomplement , IV . 4 . 3 . ( 249 ) orthogonal , II . 4 .

17 ( 72 ) and projections , ( 553 – 554 ) of a set , ( 2 ) Complemented lattice , ( 43

)

3 . 28 ( 68 ) Complement , orthocomplement , IV . 4 . 3 . ( 249 ) orthogonal , II . 4 .

17 ( 72 ) and projections , ( 553 – 554 ) of a set , ( 2 ) Complemented lattice , ( 43

)

**Complete**and o -**complete**lattice , ( 43 )**Complete**metric space , compact , 1 .### What people are saying - Write a review

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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