## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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preceding remarks that the final conclusion of the lemma is equivalent to the

preceding remarks that the final conclusion of the lemma is equivalent to the

**statement**that | det ( A ) ( A - 1x , y ) = \ y \ || A || -1 ( n - 1 ) - ( n - 1 ) / 2 . Now , since W is unitary , det ( A ) = det ( W - 1 AW ) and ( A - 1x ...Page 1756

Hence we find that if yl < r , f ( y ) = 0 , and

Hence we find that if yl < r , f ( y ) = 0 , and

**statement**( i ) is fully proved . ( B ) The uniqueness of the function V of the theorem is an evident consequence of**statement**( i ) . Moreover ,**statement**( 1 ) enables us to reduce the ...Page 1771

**Statement**( i ) follows from the preceding theorem and Theorem 6.23 .**Statement**( ii ) follows from**statement**( ii ) of the preceding theorem , since a function satisfying the hypotheses of the present**statement**( ii ) evidently ( cf.### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### 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