## Linear Operators: Spectral theory |

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Page 891

scalar function / with respect to the operator valued

chapter we shall only integrate bounded functions | and so the following

discussion of the integral will be restricted to that case . Let Ebe a field of subsets

of a set ...

scalar function / with respect to the operator valued

**set function**E . In the presentchapter we shall only integrate bounded functions | and so the following

discussion of the integral will be restricted to that case . Let Ebe a field of subsets

of a set ...

Page 894

The integral s f ( s ) E ( ds nd ) is itself a bounded additive

and thus the integral of a function g in B ( S , E ) with respect to this

written as Søg ( t ) [ $ t ( s ) E ( ds o dt ) . If f is the characteristic function of a set ...

The integral s f ( s ) E ( ds nd ) is itself a bounded additive

**set function**for 8 in E ,and thus the integral of a function g in B ( S , E ) with respect to this

**set function**iswritten as Søg ( t ) [ $ t ( s ) E ( ds o dt ) . If f is the characteristic function of a set ...

Page 1922

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Total

space of functionals , definition , V . 3 . 1 ( 418 ) Total variation of a function , I11 .

5 . 15 ( 140 ) of a

ordered ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Total

space of functionals , definition , V . 3 . 1 ( 418 ) Total variation of a function , I11 .

5 . 15 ( 140 ) of a

**set function**, III . 1 . 4 ( 97 ) . ( See also Variation ) Totallyordered ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

11 other sections not shown

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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