## Linear Operators: Spectral operators |

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Page 2300

P Then , since the collection of

bounded , it is clear from [ * ] that the collection of

T + P ) , n 2 K , is uniformly bounded . Moreover , L = 8 ( Eldin ; T ) – Elum ; T + P ...

P Then , since the collection of

**finite**sums of projections E ( / n ; T ' ) is uniformlybounded , it is clear from [ * ] that the collection of

**finite**sums of projections Elun ;T + P ) , n 2 K , is uniformly bounded . Moreover , L = 8 ( Eldin ; T ) – Elum ; T + P ...

Page 2333

( 9 ) dt des e - mto - msg Jo Jo Jo do t + s is proved to be

, 00 ) , it is sufficient by Schwarz ' s inequality to show that a du g ( t ) = / JO W 8 +

J poo f ( ut ) ds = ť t do 1 + u belongs to L2 ( 0 , 0 ) . Putting f1 ( x ) = f ( tx ) , we ...

( 9 ) dt des e - mto - msg Jo Jo Jo do t + s is proved to be

**finite**. Since f is in L2 ( 0, 00 ) , it is sufficient by Schwarz ' s inequality to show that a du g ( t ) = / JO W 8 +

J poo f ( ut ) ds = ť t do 1 + u belongs to L2 ( 0 , 0 ) . Putting f1 ( x ) = f ( tx ) , we ...

Page 2441

This shows that there exists a

lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a

constant M " independent of ε such that Lav ( 43 ) 1V4 ( , r ' ) ] + ( r , g ' ) Lav + a ...

This shows that there exists a

**finite**absolute constant c ' such that I ( 0 ) Śc ' ( 1 +lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a

**finite**constant M " independent of ε such that Lav ( 43 ) 1V4 ( , r ' ) ] + ( r , g ' ) Lav + a ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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