## Linear Operators: Spectral theory |

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Page 1175

Then K 1 is a bounded

each real $ o , let H . be the

H1 ) ( 5 ) = f ( s ) , > 60 , = 0 otherwise . By Corollary 22 , it follows that there is a ...

Then K 1 is a bounded

**mapping**of the space L ( L ( S ) ) into itself . Proof . Foreach real $ o , let H . be the

**mapping**in La ( L ( S ) ) defined by the formula ( 47 ) (H1 ) ( 5 ) = f ( s ) , > 60 , = 0 otherwise . By Corollary 22 , it follows that there is a ...

Page 1401

j - dimensional subspace S ; of Dr , and let D ; be its orthocomplement in Dr .

Define an isometric

− Ur , a c 2 . Let I , be the graph of Uj : By Theorem XII . 4 . 12 ( b ) , DIT . ) OT , is

the ...

j - dimensional subspace S ; of Dr , and let D ; be its orthocomplement in Dr .

Define an isometric

**mapping**U , of Dt onto D as follows : U ; x = Ux , 2 co , U x =− Ur , a c 2 . Let I , be the graph of Uj : By Theorem XII . 4 . 12 ( b ) , DIT . ) OT , is

the ...

Page 1736

The

) by Lemmas 3 . 22 and 3 . 23 , and evidently

from Definition 3 . 15 that it

The

**mapping**g → ¢g C is a continuous**mapping**of H ( P ) ( 8 - 11 ) into H ( P ) ( C) by Lemmas 3 . 22 and 3 . 23 , and evidently

**maps**C ( 1 ) into CO ( C ) . It followsfrom Definition 3 . 15 that it

**maps**HP8 - 11 ) into H ” ( C ) . Thus , te = fltos ...### What people are saying - Write a review

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 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 |

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