## Linear Operators, Part 2 |

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Page 889

... since the spectrum of an operator is always closed ( IX.1.5 ) , every set ... defined on the Boolean algebra B of all

... since the spectrum of an operator is always closed ( IX.1.5 ) , every set ... defined on the Boolean algebra B of all

**Borel sets**in the plane and which ...Page 894

6.2 ) that x * E ( 8 ) x O for every

6.2 ) that x * E ( 8 ) x O for every

**Borel set**8 in S and every pair x , ** with x e X , x * € X * . It follows ( II.3.15 ) that E ( S ) = 0 .Page 913

Then { on } is a decreasing sequence of

Then { on } is a decreasing sequence of

**Borel sets**such that 2 ) = v ( 0 ... To see that x is maximal let e be a**Borel set**for which ( E ( e ) x , x ) = \ E ...### 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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additive Akad 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 Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero