## Linear Operators: Spectral theory |

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Page 995

If y and f are in L ( R ) and L ( R ) respectively and if f ( m ) = 0 for every m in the

spectral set o ( 9 ) , then olf * )

with ħ ( mo ) = 1 and ħ vanishing on an open set

p ) .

If y and f are in L ( R ) and L ( R ) respectively and if f ( m ) = 0 for every m in the

spectral set o ( 9 ) , then olf * )

**contains**no isolated points ... Let h be in L ( R )with ħ ( mo ) = 1 and ħ vanishing on an open set

**containing**the remainder of olf *p ) .

Page 996

From Lemma 12 ( b ) it is seen that olf * ) Colp ) and from Lemma 12 ( c ) and the

equation of = tf it follows that olf * 9 )

* ) is a closed subset of the boundary of o ( q ) . Since f * 9 = 0 it follows from ...

From Lemma 12 ( b ) it is seen 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 boundary of o ( q ) . Since f * 9 = 0 it follows from ...

Page 1456

Suppose for definiteness that I

, so that , unless I1 = I ( in which case t = t , and is evidently bounded below ) , I ,

Suppose for definiteness that I

**contains**a neighborhood of the left end point a of I, so that , unless I1 = I ( in which case t = t , and is evidently bounded below ) , I ,

**contains**a neighborhood of the right end point b of 1 . Unless 12 = I , in which ...### What people are saying - Write a review

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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