## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1024

+ N Since ( 1 / N ) | tr ( B ) | < 1 and 1 # Axe , the inverse operator ( I – By ) -1

exists and it is readily

11 = | ( I– By ) -1 ) and so ( ii ) det ( I – Bx ) || ( I – B ) -1 ) = \ det ( I – Bx ) || ( 1 - Bx )

-11 .

+ N Since ( 1 / N ) | tr ( B ) | < 1 and 1 # Axe , the inverse operator ( I – By ) -1

exists and it is readily

**seen**that 1 ( 1 - B ) -1x , ( 1+ tr ( B ) N Therefore | ( I – B ) -11 = | ( I– By ) -1 ) and so ( ii ) det ( I – Bx ) || ( I – B ) -1 ) = \ det ( I – Bx ) || ( 1 - Bx )

-11 .

Page 1154

Since it is clear that ( 2 ) = Ex £ , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) =

c ( 2x2 ) ( E ) , Εε Σ ( 2 ) , for some constant c independent of E. This condition ( i )

, as is

Since it is clear that ( 2 ) = Ex £ , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) =

c ( 2x2 ) ( E ) , Εε Σ ( 2 ) , for some constant c independent of E. This condition ( i )

, as is

**seen**from Corollary III.11.6 , is a consequence of the assertion that 2 ( 2 ) ...Page 1324

Nelson Dunford, Jacob T. Schwartz. it is

equations are equivalent to the relation f ( t ) = { « ; ( t ) F ( 1,9 * ) – B ( t ) F , ( 1 , vt

) , 1 € C " ~ ( ) . Define ai Qi , i 1 , ... , u * , a ; = Bi - u * , i u * +1 , ... , n and ni = 2 * , i

...

Nelson Dunford, Jacob T. Schwartz. it is

**seen**from Lemma 4 ( c ) that the jumpequations are equivalent to the relation f ( t ) = { « ; ( t ) F ( 1,9 * ) – B ( t ) F , ( 1 , vt

) , 1 € C " ~ ( ) . Define ai Qi , i 1 , ... , u * , a ; = Bi - u * , i u * +1 , ... , n and ni = 2 * , i

...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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