## Linear Operators: General theory |

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Page 364

( U , A ) Km ( + ) dt , where Km ( t ) is Km ( 0 , t ) in the notation of

Here f ... 1 / 2pins , Tmt → f in the norm of L , ( or AC , or C ( n ) ) for f € Lp ( or AC ,

or ( ( n ) ) if Tmi → f in the norm of C for each fe C. ( Hint : Use

49. ) ...

( U , A ) Km ( + ) dt , where Km ( t ) is Km ( 0 , t ) in the notation of

**Exercise**34. (Here f ... 1 / 2pins , Tmt → f in the norm of L , ( or AC , or C ( n ) ) for f € Lp ( or AC ,

or ( ( n ) ) if Tmi → f in the norm of C for each fe C. ( Hint : Use

**Exercises**35 and49. ) ...

Page 365

Show that the map : f → $ defined in

manner onto the closed subspace of L , consisting of those F all of whose

negative Fourier coefficients vanish . 55 Using the notations of

54 ...

Show that the map : f → $ defined in

**Exercise**53 maps H , in a linear one - onemanner onto the closed subspace of L , consisting of those F all of whose

negative Fourier coefficients vanish . 55 Using the notations of

**Exercises**53 and54 ...

Page 371

( Hint : Generalize the argument of

of the unit disc . ) Show that

H , can be written as a product gh , where g and h are in Hg . ( Hint : C'se ...

( Hint : Generalize the argument of

**Exercise**85 to apply to zeros on the boundaryof the unit disc . ) Show that

**Exercise**87 is valid even if p 1 . 89 Every function f inH , can be written as a product gh , where g and h are in Hg . ( Hint : C'se ...

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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