## Linear Operators: Spectral theory |

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Page 993

Then it

. , Qy is independent of V . Q . E . D . 16 THEOREM . If the bounded measurable

function o has its spectral set consisting of the single point m then , for some ...

Then it

**follows**from what has just been demonstrated that ay , = Qyuv , = Qy , i . e. , Qy is independent of V . Q . E . D . 16 THEOREM . If the bounded measurable

function o has its spectral set consisting of the single point m then , for some ...

Page 996

1 ( d ) it

seen that olf * ) Colp ) and from Lemma 12 ( c ) and the equation of = tf it

that olf * 9 ) contains no interior point of o ( 9 ) . Hence of * ) is a closed subset of

the ...

1 ( d ) it

**follows**from the above equation that f * 4 0 . From Lemma 12 ( b ) it isseen that olf * ) Colp ) and from Lemma 12 ( c ) and the equation of = tf it

**follows**that olf * 9 ) contains no interior point of o ( 9 ) . Hence of * ) is a closed subset of

the ...

Page 1486

If

6 . 35 , it

19 , T has no boundary values . Thus , by Definition 2 . 17 every linear ...

If

**follows**immediately that all the coefficients of t are bounded ; thus , by Theorem6 . 35 , it

**follows**that t has no boundary values at + 00 or at – 00 . By Theorem 2 .19 , T has no boundary values . Thus , by Definition 2 . 17 every linear ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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