## Linear Operators: Spectral theory |

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Page 984

The set of functions f in Ly ( R ) for which f

is dense in Ly ( R ) . PROOF . It follows from Lemma 3 . 6 that the set of all

functions in L2 ( R , B , u ) which

space ...

The set of functions f in Ly ( R ) for which f

**vanishes**in a neighborhood of infinityis dense in Ly ( R ) . PROOF . It follows from Lemma 3 . 6 that the set of all

functions in L2 ( R , B , u ) which

**vanish**outside of compact sets is dense in thisspace ...

Page 997

Let o be a bounded measurable function on R . Then a point m , in R is in the

complement of the spectral set of u if and only if there are neighborhoods V of the

identity in R and U of m , such that the transform t ( of )

in ...

Let o be a bounded measurable function on R . Then a point m , in R is in the

complement of the spectral set of u if and only if there are neighborhoods V of the

identity in R and U of m , such that the transform t ( of )

**vanishes**on U for every fin ...

Page 1650

If F

parts of this lemma are left to the reader as an exercise . To prove ( v ) , we must

show from our hypothesis that F ( q ) = 0 if q is in CO ( U . 12 ) . Let K be a

compact ...

If F

**vanishes**in each set Iç , it**vanishes**in Uqla Proof . The proofs of the first fourparts of this lemma are left to the reader as an exercise . To prove ( v ) , we must

show from our hypothesis that F ( q ) = 0 if q is in CO ( U . 12 ) . Let K be a

compact ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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