## Linear Operators: Spectral theory |

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It follows then from ( iii ) that the projections Ed ) also commute with T ( f ) and this completes the proof of the theorem . Q.E.D. 3 COROLLARY . The spectral measure is countably additive in the strong operator

It follows then from ( iii ) that the projections Ed ) also commute with T ( f ) and this completes the proof of the theorem . Q.E.D. 3 COROLLARY . The spectral measure is countably additive in the strong operator

**topology**. Proof .Page 922

**topology**, i.e. , Tnx → Tx for every x in the space upon which the operators T , T1 , T2 , ... , are defined . 1 LEMMA . Let S , T , Sn , Tn , n 21 be bounded linear operators in Hilbert space with Sn → S , T , → T in the strong ...Page 1921

F ( 1550 ) Subadditive function , definition , ( 618 ) Subbase for a

F ( 1550 ) Subadditive function , definition , ( 618 ) Subbase for a

**topology**, 1.4.6 ( 10 ) criterion for , 1.4.8 ( 11 ) Subspace , of a linear space , ( 36 ) . ( See also Manifold ) Summability , of Fourier series , IV.14.34-51 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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