## Linear Operators: Spectral theory |

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Page 861

Clearly if x - 1

' ) ] = 4 , ( T ; ' ) = = T , ' ( ga ) , and if a = T le , then az = T ; lz for every z e X . Also

xa = Tya = e = T ; ? ( T2e ) = T ( ex ) = ( T ; e ) x = ax . Thus x - 1

Clearly if x - 1

**exists**then Tr - Tc = T & T2 - 1 = 1 . If Til**exists**in B ( x ) , then TE ( T' ) ] = 4 , ( T ; ' ) = = T , ' ( ga ) , and if a = T le , then az = T ; lz for every z e X . Also

xa = Tya = e = T ; ? ( T2e ) = T ( ex ) = ( T ; e ) x = ax . Thus x - 1

**exists**and Trx ...Page 1057

Thus ( 2 ) gives j→ Jen y " ^ 27 F ( K * f ) ( u ) = ( 27 ) - 1 / 2 lim PL 1197 x ( y ) { |

ciua f ( – y ) dx ) dy = { uim a la supervdy ) Fury ) , provided only that the limit in

the braces in this last equation

...

Thus ( 2 ) gives j→ Jen y " ^ 27 F ( K * f ) ( u ) = ( 27 ) - 1 / 2 lim PL 1197 x ( y ) { |

ciua f ( – y ) dx ) dy = { uim a la supervdy ) Fury ) , provided only that the limit in

the braces in this last equation

**exists**. Thus , to complete the proof of the present...

Page 1262

Then there

such that Ax = PQx , XEH , P denoting the orthogonal projection of Hi on H . 29

Let { Tn } be a sequence of bounded operators in Hilbert space H . Then there

Then there

**exists**a Hilbert space H , 2H , and an orthogonal projection Q in H ,such that Ax = PQx , XEH , P denoting the orthogonal projection of Hi on H . 29

Let { Tn } be a sequence of bounded operators in Hilbert space H . Then there

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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