## Linear Operators: Spectral theory |

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Page 970

If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) ,

then Zef is in Ly ( R ) n L2 ( R ) and f is the

generalized sequence { Xef } . Hence , by Theorem 9 , tf is the

L ( M ) ...

If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) ,

then Zef is in Ly ( R ) n L2 ( R ) and f is the

**limit**in the norm of L2 ( R ) of thegeneralized sequence { Xef } . Hence , by Theorem 9 , tf is the

**limit**in the norm ofL ( M ) ...

Page 976

... William G. Bade, Robert G. Bartle. By using the form of the characters on RTM

the Plancherel theorem may be given a more concrete formulation in the present

case also . It is easily seen that this theorem asserts that if f is in L ( R ” ) , the

...

... William G. Bade, Robert G. Bartle. By using the form of the characters on RTM

the Plancherel theorem may be given a more concrete formulation in the present

case also . It is easily seen that this theorem asserts that if f is in L ( R ” ) , the

**limit**...

Page 1124

Thus , it follows as above that Em = E . This proves that if y ( En ) is increasing

with

way that if P ( En ) is decreasing with the

Thus , it follows as above that Em = E . This proves that if y ( En ) is increasing

with

**limit**( E ) , then E , has the strong**limit**E . We may show in exactly the sameway that if P ( En ) is decreasing with the

**limit**q ( E ) , then En has the ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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