## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 82

Page 897

It follows then from ( iii ) that the projections E ( 8 ) 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 E ( 8 ) 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

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

57 other sections not shown

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero