## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Self Adjoint Operators in Hilbert Space. Spectral theory. Part II Nelson Dunford,

Jacob T. Schwartz. preceding remarks that the final conclusion of the lemma is

equivalent to the

- 1 ) ...

Self Adjoint Operators in Hilbert Space. Spectral theory. Part II Nelson Dunford,

Jacob T. Schwartz. preceding remarks that the final conclusion of the lemma is

equivalent to the

**statement**that | det ( A ) ( A - 1x , y ) = \ y \ || A || n - 1 ( n - 1 ) - ( n- 1 ) ...

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and Fin H ( +1 ) ( I ) , ( cf. Definition 15 ( i ) ) . To prove ( ii ) and the final

of the lemma , we first note that it is evident for k 20 from Definition 15 ( i ) .

**Statement**( iii ) follows from**statement**( ii ) and the fact that Flu + 1 Flv for all k 20and Fin H ( +1 ) ( I ) , ( cf. Definition 15 ( i ) ) . To prove ( ii ) and the final

**statement**of the lemma , we first note that it is evident for k 20 from Definition 15 ( i ) .

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To prove this

} , a being chosen so large that C 21. Making a dilation of coordinates ( cf.

Lemma 3.48 ) , we may and shall suppose without loss of generality that a = n .

To prove this

**statement**, let C be a cube of the form C = { x € E " | \ x , < a , 1 , ... , n} , a being chosen so large that C 21. Making a dilation of coordinates ( cf.

Lemma 3.48 ) , we may and shall suppose without loss of generality that a = n .

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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