## Linear Operators, Part 2 |

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Page 984

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

dense in Li ( R ) . PROOF . It follows from Lemma 3.6 that the set of all functions in

L2 ( R , B , u ) which

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

**vanishes**in a neighborhood of infinity isdense in Li ( 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 this space ...Page 993

It remains to be proved that the number ay is independent of the open set V. If f is

in L ( R ) , L ( R ) , f

open subset V , of V , then the above proof shows that ( of ) ( m ) = Qy for every m

...

It remains to be proved that the number ay is independent of the open set V. If f is

in L ( R ) , L ( R ) , f

**vanishes**on the complement of V , and f ( m ) = 1 for m in anopen subset V , of V , then the above proof shows that ( of ) ( m ) = Qy for every m

...

Page 997

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

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

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

in L ...

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

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

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

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

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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