## Linear Operators: Spectral theory |

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Page 1105

We have tr ( T ) = f ' ( T ) , where fr ( T ) is the expression of

now pause to sharpen another of the inequalities of

, E C , , A , C , A , EC , there ri ' + r ; " + rg = 1 . Then ( a ) tr ( A , A , A3 ) < All1 , A2 |

...

We have tr ( T ) = f ' ( T ) , where fr ( T ) is the expression of

**Lemma**13 ( b ) . Wenow pause to sharpen another of the inequalities of

**Lemma**9 . 20**LEMMA**. Let A, E C , , A , C , A , EC , there ri ' + r ; " + rg = 1 . Then ( a ) tr ( A , A , A3 ) < All1 , A2 |

...

Page 1226

Proof . Part ( a ) follows immediately from

immediately from part ( a ) and

b ) that any symmetric operator with dense domain has a unique minimal closed

...

Proof . Part ( a ) follows immediately from

**Lemma**5 ( b ) , and part ( b ) followsimmediately from part ( a ) and

**Lemma**5 ( c ) . Q . E . D . It follows from**Lemma**6 (b ) that any symmetric operator with dense domain has a unique minimal closed

...

Page 1698

Using

by

V ) , so that in case ( a ) we have shown that fooi ? is the limit in the norm of H ...

Using

**Lemma**2 . 1 , let y be a function in CO ( V ) with y ( x ) = 1 for x in K . Then ,by

**Lemmas**3 . 22 and 3 . 10 , fonil = y ( foqil ) = limm + yhm in the norm of H ( P ) (V ) , so that in case ( a ) we have shown that fooi ? is the limit in the norm of H ...

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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 |

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