## Linear Operators: Spectral theory |

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Page 861

Clearly if x - 1

= y ) 2 ] = yz , ( T ? ' y ) 2 = T ? ? ( yz ) , and if a = Tole , then az = Tölz for every z e

X . Also xa = Tja = e = T , ' ( Toe ) = 1 ; } ( ex ) = ( T72e ) x = ax . Thus x - 1

Clearly if x - 1

**exists**then Tr - Tc = T 72 - 1 = 1 . If Til**exists**in B ( X ) , then T { [ ( T= y ) 2 ] = yz , ( T ? ' y ) 2 = T ? ? ( yz ) , and if a = Tole , then az = Tölz for every z e

X . Also xa = Tja = e = T , ' ( Toe ) = 1 ; } ( ex ) = ( T72e ) x = ax . Thus x - 1

**exists**...Page 1057

Thus ( 2 ) gives [ 2 ( y ) P Jen ly " F ( K * f ) ( u ) = ( 27 ) - n / 2 lim j + iux f ( x , y ) dx

dy RA - { Him a po zasemanato PUYw , provided only that the limit in the braces

in this last equation

Thus ( 2 ) gives [ 2 ( y ) P Jen ly " F ( K * f ) ( u ) = ( 27 ) - n / 2 lim j + iux f ( x , y ) dx

dy RA - { Him a po zasemanato PUYw , provided only that the limit in the braces

in this last equation

**exists**. Thus , to complete the proof of the present lemma , it ...Page 1261

23 If an operator T has a closed linear extension there

linear extension T such that if T , is any closed linear extension of T then ICT . T is

called the closure of T . ( a ) There

closed ...

23 If an operator T has a closed linear extension there

**exists**a unique closedlinear extension T such that if T , is any closed linear extension of T then ICT . T is

called the closure of T . ( a ) There

**exists**a densely defined operator with noclosed ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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