## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2239

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Since f Xe is a bounded function , the operator T ( f Xe ) is a

bounded operator . If x is in E ( 7 ) X as well as in E ( e ) X , it

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Since f Xe is a bounded function , the operator T ( f Xe ) is a

bounded operator . If x is in E ( 7 ) X as well as in E ( e ) X , it

**follows**from the ...Page 2246

it

domain of C . It is clear then that ( XI – C ) R ( a ) = x for x in H and R ( a ) ( 21 – C

) x = x for x in D ( C ) , so that R ( a ) = R ( a ; C ) and 1 € ( C ) . On the other hand ,

if X ...

it

**follows**that R ( 1 ) is a bounded operator whose range is contained in thedomain of C . It is clear then that ( XI – C ) R ( a ) = x for x in H and R ( a ) ( 21 – C

) x = x for x in D ( C ) , so that R ( a ) = R ( a ; C ) and 1 € ( C ) . On the other hand ,

if X ...

Page 2459

We leave the details of the similar proofs that ( V1 , vz ) = 0 ) = ( v2 , v3 ) to the

reader , and conclude without further ado that Lac ( H ) , Esing ( H ) , and C ( H )

are mutually orthogonal . Statement ( b ) of our lemma

H ) ...

We leave the details of the similar proofs that ( V1 , vz ) = 0 ) = ( v2 , v3 ) to the

reader , and conclude without further ado that Lac ( H ) , Esing ( H ) , and C ( H )

are mutually orthogonal . Statement ( b ) of our lemma

**follows**at once . If xn Lac (H ) ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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