## Linear Operators: Spectral theory |

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Page 993

Now let V , be an arbitrary open subset of Ř with compact closure . Then it

from what has just been demonstrated that av , = oyuv , = Qy , i.e. , Qy is

independent of V. Q.E.D. 0 16 THEOREM . If the bounded measurable function o

has its ...

Now let V , be an arbitrary open subset of Ř with compact closure . Then it

**follows**from what has just been demonstrated that av , = oyuv , = Qy , i.e. , Qy is

independent of V. Q.E.D. 0 16 THEOREM . If the bounded measurable function o

has its ...

Page 996

Since f * q is continuous by Lemma 3.1 ( d ) it

that f * 9 +0 . From Lemma 12 ( b ) it is seen that olf * o ) Colo ) and from Lemma

12 ( c ) and the equation of = Tf it

...

Since f * q is continuous by Lemma 3.1 ( d ) it

**follows**from the above equationthat f * 9 +0 . From Lemma 12 ( b ) it is seen that olf * o ) Colo ) and from Lemma

12 ( c ) and the equation of = Tf it

**follows**that o ( f * ) contains no interior point of o...

Page 1124

That is , Q ( E ) = Q ( E ) implies E = E. Similarly , y ( E ) SQ ( E ) implies ESE . If En

, E are in F and q ( En ) increases to the limit ( E ) , then it

have already proved that En is an increasing sequence of projections and En > E

.

That is , Q ( E ) = Q ( E ) implies E = E. Similarly , y ( E ) SQ ( E ) implies ESE . If En

, E are in F and q ( En ) increases to the limit ( E ) , then it

**follows**from what wehave already proved that En is an increasing sequence of projections and En > E

.

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

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