## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2152

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

Theodore Schwartz. To

and let M ( S ) = { 2 x € X , ( x ) Ş8 } . It will be shown that M ( 8 ) is closed .

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

Theodore Schwartz. To

**prove**( C ) , let d be a closed subset of the complex planeand let M ( S ) = { 2 x € X , ( x ) Ş8 } . It will be shown that M ( 8 ) is closed .

Page 2236

To

since T | Elen ) X is bounded , statements ( i ) and ( ii ) and the functional calculus

of bounded operators ( cf . VII . 3 . 10 ) may be applied to conclude that lim ( f + g )

...

To

**prove**( vi ) , let x be in D ( f ( T ) + g ( T ) ) and let { en } be as above . Then ,since T | Elen ) X is bounded , statements ( i ) and ( ii ) and the functional calculus

of bounded operators ( cf . VII . 3 . 10 ) may be applied to conclude that lim ( f + g )

...

Page 2459

If xn e Lac ( H ) and limn + Xn = x , then , by what we have already

may write x = y1 + y2 + Ys , where yı e Lac ( H ) and Y2 , Y3 are orthogonal to Lac

( H ) ... Using this last fact , it is easy to

If xn e Lac ( H ) and limn + Xn = x , then , by what we have already

**proved**, wemay write x = y1 + y2 + Ys , where yı e Lac ( H ) and Y2 , Y3 are orthogonal to Lac

( H ) ... Using this last fact , it is easy to

**prove**assertion ( c ) of the present lemma .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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