## Linear Operators: Spectral theory |

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Page 961

= S , F ( 0 – 2 ) y ( x ) dx = ( 4 * * ) ( 0 ) = 0 ( f * y ) . Since the operation T ( ) of

convolution by f commutes with E ( e ) and since , as we have seen in the

...

**Proof**. If we write y for y ( e ) , then ( t , x ) = { 2 } ( 2 ) ¥ ( x ) dx = Sa tla – 0 ) ¥ ( ) dx= S , F ( 0 – 2 ) y ( x ) dx = ( 4 * * ) ( 0 ) = 0 ( f * y ) . Since the operation T ( ) of

convolution by f commutes with E ( e ) and since , as we have seen in the

**proof**of...

Page 1012

from which it follows that | | T - Tmll Sɛ for m > m ( s ) and completes the

HS is a B - space under the Hilbert - Schmidt norm . Finally , let T be in HS and let

B be any bounded linear operator in H . Then GEA αε Α | | BT | | * = E \ BTxal ?

from which it follows that | | T - Tmll Sɛ for m > m ( s ) and completes the

**proof**thatHS is a B - space under the Hilbert - Schmidt norm . Finally , let T be in HS and let

B be any bounded linear operator in H . Then GEA αε Α | | BT | | * = E \ BTxal ?

Page 1708

... Alm + P ) ( C ) . Hence , since g ( x ) = 1 for x in E14 , it follows from Lemmas 3 .

9 and 3 . 23 that the restriction fs Eve belongs to A ( m + P ) ( E14 ) . Thus ( cf . 3 .

48 ) fegy belongs to A ( m + P ) ( Egja ) , and the

... Alm + P ) ( C ) . Hence , since g ( x ) = 1 for x in E14 , it follows from Lemmas 3 .

9 and 3 . 23 that the restriction fs Eve belongs to A ( m + P ) ( E14 ) . Thus ( cf . 3 .

48 ) fegy belongs to A ( m + P ) ( Egja ) , and the

**proof**of Lemma 3 is complete .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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