## Linear Operators: Spectral theory |

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Page 1190

If T is an

Lemma 6 ( a ) T is closed and by the closed graph theorem ( II . 2 . 4 ) , T is

bounded . Thus an

If T is an

**everywhere**defined symmetric operator then T * ] T and thus T * = T . ByLemma 6 ( a ) T is closed and by the closed graph theorem ( II . 2 . 4 ) , T is

bounded . Thus an

**everywhere**defined symmetric operator is bounded and self ...Page 1212

Then Jen + 1 Sa + 1 Sc ( Bn + 17 ) ( 4 ) F ( a ) u ( da ) = Ss . f ( s ) ( 4n + 1 F ) ( 8 ) v

( ds ) = 5s . ( ) ( F ( T ) g ) ( s ) v ( ds ) = s t ( s ) ( A , F ) ( s ) v ( ds ) nd ) ( 2 ) F ( 2 ) u

( da ) . Thus , ( Bn + 11 ) ( a ) = ( B - 1 ) ( a ) u - almost

Then Jen + 1 Sa + 1 Sc ( Bn + 17 ) ( 4 ) F ( a ) u ( da ) = Ss . f ( s ) ( 4n + 1 F ) ( 8 ) v

( ds ) = 5s . ( ) ( F ( T ) g ) ( s ) v ( ds ) = s t ( s ) ( A , F ) ( s ) v ( ds ) nd ) ( 2 ) F ( 2 ) u

( da ) . Thus , ( Bn + 11 ) ( a ) = ( B - 1 ) ( a ) u - almost

**everywhere**on en .Page 1233

Then ( T1 - 201 ) - 1 = R ( 20 ) is an

norm not more than TI ( 20 ) 1 - 1 . Consequently , the series in + 1 [ * ] Ź ( – 10 ) "

R ( * + 2 n = 0 converges if 12 - hol < \ I ( 2011 . Since T , is closed , we have ( T ...

Then ( T1 - 201 ) - 1 = R ( 20 ) is an

**everywhere**defined , bounded operator ofnorm not more than TI ( 20 ) 1 - 1 . Consequently , the series in + 1 [ * ] Ź ( – 10 ) "

R ( * + 2 n = 0 converges if 12 - hol < \ I ( 2011 . Since T , is closed , we have ( T ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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