## Linear Operators: Spectral theory |

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Results 1-3 of 82

Page 1297

The first

Now T ( T ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T ( ) ) is

complete in the

as ...

The first

**norm**is the**norm**of the pair [ 1 , T / ] as an element of the graph of T ( T ) .Now T ( T ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T ( ) ) is

complete in the

**norm**Iflı . Since the two additional terms in 112 are the**norm**of fas ...

Page 1431

Because 8ml2 + 0 , it follows that go ! 0 for 0 Sk < n and therefore also that k = 0 2

• n - 1 12 k = 0 By [ * ] this implies that langin ) ja →0 , and since la , ( • ) - 1 is

bounded by hypothesis , loom ! 12 + 0 . Thus { & m } converges to zero in the

Because 8ml2 + 0 , it follows that go ! 0 for 0 Sk < n and therefore also that k = 0 2

• n - 1 12 k = 0 By [ * ] this implies that langin ) ja →0 , and since la , ( • ) - 1 is

bounded by hypothesis , loom ! 12 + 0 . Thus { & m } converges to zero in the

**norm**...Page 1639

1 + ulf ; J , m ) This

- space . If k < oo and I is compact , but not otherwise , the spaces Cl ( 1 ) and Cr (

I ) are B - spaces under a

1 + ulf ; J , m ) This

**norm**makes each of the spaces listed above into a complete F- space . If k < oo and I is compact , but not otherwise , the spaces Cl ( 1 ) and Cr (

I ) are B - spaces under a

**norm**equivalent to the**norm**displayed , though not ...### 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

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