## Linear Operators, Part 2 |

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Page 888

Here we have used the notations A - B and Av B for the intersection and

Here we have used the notations A - B and Av B for the intersection and

**union**of two commuting projections A and B. We recall that these operators are defined by the equations AB = AB , Av B = A + B - AB and that the intersection and ...Page 958

The set function Mo will now be extended to a countably additive function u on B. Let e be a set in B. If e is contained in the

The set function Mo will now be extended to a countably additive function u on B. Let e be a set in B. If e is contained in the

**union**of an increasing sequence { en } of sets in B , let ( * ) μ ( e ) = lim po ( een ) , so that n and ...Page 1343

for leen - Up = ien , it is clear that functions acis and Vi satisfy the requirements ( a ) and ( b ) of the lemma for all a in the set Un- en Since u is o - finite the real axis is the

for leen - Up = ien , it is clear that functions acis and Vi satisfy the requirements ( a ) and ( b ) of the lemma for all a in the set Un- en Since u is o - finite the real axis is the

**union**of a sequence of sets of finite u - measure ...### 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