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

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Page 2300

Then , since the collection of

bounded , it is clear from [ * ] that the collection of

; T + P ) , n 2 K , is uniformly bounded . Moreover , Erap ( Elan ; T ) – Elun ; T + P ...

Then , since the collection of

**finite**sums of projections E ( n ; T ' ) is uniformlybounded , it is clear from [ * ] that the collection of

**finite**sums of projections E ( Mn; T + P ) , n 2 K , is uniformly bounded . Moreover , Erap ( Elan ; T ) – Elun ; T + P ...

Page 2333

Hence , in view of the Fubini theorem , the proof of ( a ) will be complete as soon

as the quantity popoo $ $ $ e - mée - mof ( e ) f ( s ) dt ds dm = $ 10 $ 401 ( 9 ) dt

ds do Jo Jo is proved to be

Hence , in view of the Fubini theorem , the proof of ( a ) will be complete as soon

as the quantity popoo $ $ $ e - mée - mof ( e ) f ( s ) dt ds dm = $ 10 $ 401 ( 9 ) dt

ds do Jo Jo is proved to be

**finite**. Since f is in L2 ( 0 , 0 ) , it is sufficient by ...Page 2441

This shows that there exists a

lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a

constant M " independent of ε such that ( 43 ) 17 6 . + younger og levererar o ...

This shows that there exists a

**finite**absolute constant c ' such that 1 ( a ) c ' ( 1 +lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a

**finite**constant M " independent of ε such that ( 43 ) 17 6 . + younger og levererar o ...

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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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analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero