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

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Page 2236

Then , since TE ( en ) X is bounded ,

calculus of bounded operators ( cf. ... In the first case described in

o ( T ) is a compact subset of U , and by Corollary XV.3.5 , ( o ( T ) ) == I so that ...

Then , since TE ( en ) X is bounded ,

**statements**( i ) and ( ii ) and the functionalcalculus of bounded operators ( cf. ... In the first case described in

**statement**( v ) ,o ( T ) is a compact subset of U , and by Corollary XV.3.5 , ( o ( T ) ) == I so that ...

Page 2239

Moreover ,

Letting e e E , and x e E ( e ) X , we have T ' ( fxe ) = lim T ' ( fxe ) E ( en ) x = lim T (

fXe Xenda = lim T ( fxenda = T ( f ) x by the operational calculus for bounded ...

Moreover ,

**statement**( g ) follows from Corollary 7 .**Statement**( d ) is obvious .Letting e e E , and x e E ( e ) X , we have T ' ( fxe ) = lim T ' ( fxe ) E ( en ) x = lim T (

fXe Xenda = lim T ( fxenda = T ( f ) x by the operational calculus for bounded ...

Page 2476

We therefore see that , as asserted ,

that gi ( a ) = 0 for all a key . Since ( H + V , H ) is a closed subspace of H ' ( cf.

Lemma 2 ) it follows that every ĝ e H ' such that g : ( a ) = 0 for all a e e , belongs

to ...

We therefore see that , as asserted ,

**statement**( 76 ) holds for each s e H ' suchthat gi ( a ) = 0 for all a key . Since ( H + V , H ) is a closed subspace of H ' ( cf.

Lemma 2 ) it follows that every ĝ e H ' such that g : ( a ) = 0 for all a e e , belongs

to ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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