## Linear Operators: Spectral theory |

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Page 893

It is clear that if v is a bounded

integral S / ( s ) o ( ds ) of a bounded E - measurable function f may be defined

similarly . Thus if E is a bounded

are ...

It is clear that if v is a bounded

**additive**vector valued set function on E , theintegral S / ( s ) o ( ds ) of a bounded E - measurable function f may be defined

similarly . Thus if E is a bounded

**additive**set function on £ whose values E ( S )are ...

Page 932

Sz . - Nagy's original proof depended on the following theorem due to Neumark (

3 ] . 271 eine F ( do ) , 0 THEOREM . Let S be an abstract set and E a field ( resp .

o - field ) of subsets of S. Let F be an

...

Sz . - Nagy's original proof depended on the following theorem due to Neumark (

3 ] . 271 eine F ( do ) , 0 THEOREM . Let S be an abstract set and E a field ( resp .

o - field ) of subsets of S. Let F be an

**additive**( resp . weakly countably**additive**)...

Page 958

This argument shows that the vector valued

countably

is countably

this ...

This argument shows that the vector valued

**additive**set function y is weaklycountably

**additive**on the o - field consisting ... By a theorem of Pettis ( IV.10.1 ) itis countably

**additive**in the strong topology , i.e. , ly ( rn ) / 2 = Molim ) → 0 , andthis ...

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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