## 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. borhoods of s , and U , the neighborhoods of 8g . For U EU , i

= 1 , 2 , let W ( U1 , U2 ) = U , n

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

Jacob T. Schwartz. borhoods of s , and U , the neighborhoods of 8g . For U EU , i

= 1 , 2 , let W ( U1 , U2 ) = U , n

**R**+ U , n**R**, where the sum is taken**in R**and the ...Page 948

From the continuity of the fact that

, we conclude immediately that s 0 = 8 , 8 , 8 , = 82 8 , and $ 1 = ( s2 = sz ) ( 81 82

) Sz . It remains to be shown that inverse elements under exist in S. Consider ...

From the continuity of the fact that

**R**is dense in S , and that coincides with +**on R**, we conclude immediately that s 0 = 8 , 8 , 8 , = 82 8 , and $ 1 = ( s2 = sz ) ( 81 82

) Sz . It remains to be shown that inverse elements under exist in S. Consider ...

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Since I ( x , u )

one way as a product T PA , where P is a partial isometry whose initial domain is

.

Since I ( x , u )

**R**( x , iv ) , it follows that ( x , v ) ( Px , Pv ) if x , V EM . ... and onlyone way as a product T PA , where P is a partial isometry whose initial domain is

**R**( T * ) , and A is a positive self adjoint transformation such that**R**( A ) =**R**( T * ).

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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