## Linear Operators: General theory |

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Page 364

... operator Tm is given by the integral Tmf = 80 * ( U , 7 ) Km ( t ) dt , where Km ( t

) is Km ( 0 , t ) in the notation of

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

... operator Tm is given by the integral Tmf = 80 * ( U , 7 ) Km ( t ) dt , where Km ( t

) is Km ( 0 , t ) in the notation of

**Exercise**34 . ... or C \ n ) ) for f e Lp ( or AC , or C \n ) ) if Tmt →f in the norm of C for each fe C . ( Hint : Use

**Exercises**35 and 49 . ) ...Page 365

55 Using the notations of

) = | ( reio ) , then Urf - fp → 0 as r →1 . ... sup { S3 * | ( reio ) | pdop1 / p , H ,

becomes a reflexive Banach space . r < 1 58 Using

Lp ...

55 Using the notations of

**Exercises**53 and 54 , show that if je H , and if ( 0 , 1 ) ( 0) = | ( reio ) , then Urf - fp → 0 as r →1 . ... sup { S3 * | ( reio ) | pdop1 / p , H ,

becomes a reflexive Banach space . r < 1 58 Using

**Exercise**19 , show that if F €Lp ...

Page 371

( Hint : Generalize the argument of

of the unit disc . ) 88 Show that

function f in H , can be written as a product gh , where g and h are in Hz . ( Hint :

Use ...

( Hint : Generalize the argument of

**Exercise**85 to apply to zeros on the boundaryof the unit disc . ) 88 Show that

**Exercise**87 is valid even if p = 1 . 89 Everyfunction f in H , can be written as a product gh , where g and h are in Hz . ( Hint :

Use ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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