## Linear Operators: General theory |

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Page 138

inn i = n

proving that u ( E ) = u ( En ) . Q . E . D . n = 1 14 THEOREM . Let u be a bounded

...

**Consequently**, Lil v ( u , E ; ) < oo , and vlu , UE : ) = v ( u , E ; ) + 0 , as n → 00 .inn i = n

**Consequently**, - 1 Tu ( E ) – Eu ( E ; ) ] = lu ( UE ; ) = v ( u , u E ; ) → 0 ,proving that u ( E ) = u ( En ) . Q . E . D . n = 1 14 THEOREM . Let u be a bounded

...

Page 151

' + 2ello Slim sup [ { S \ / « ( 8 ) — t ( s ) [ po ( ja , ds ) " + { S . . \ tm ( 8 ) – ( 8 ) | Pv (

, ds ) ) 1 / 07 + 2e1 / p = 2£110 , so that lim \ n - Imlp = 0 . Since L ( S , E , M ...

**Consequently**, lim sup \ tn - Imlo Slim sup { St . \ \ n ( s ) — fm ( s ) | Posu , ds ) } \ '' + 2ello Slim sup [ { S \ / « ( 8 ) — t ( s ) [ po ( ja , ds ) " + { S . . \ tm ( 8 ) – ( 8 ) | Pv (

, ds ) ) 1 / 07 + 2e1 / p = 2£110 , so that lim \ n - Imlp = 0 . Since L ( S , E , M ...

Page 369

most n + 1 points - 1 Sh Sta . . . < tk § 1 , and there are constants c1 , . . . , Ch with

Lil leil = \ , and in terms of which we may write an “ interpolation formula ” f ( x ) ...

**Consequently**, unless xo ( t ) is a constant of absolute value 1 , C is a set of atmost n + 1 points - 1 Sh Sta . . . < tk § 1 , and there are constants c1 , . . . , Ch with

Lil leil = \ , and in terms of which we may write an “ interpolation formula ” f ( x ) ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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