## Linear Operators: Spectral theory |

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scalar functions 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 be a field of subsets

of a set ...

scalar functions 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 be a field of subsets

of a set ...

Page 1899

13 ( 138 ) Absolutely continuous functions , defi . on C ( S ) convergence of

bounded nition , IV . 2 . 22 ( 242 ) additive

See Continuous set ( 316 ) function and

13 ( 138 ) Absolutely continuous functions , defi . on C ( S ) convergence of

bounded nition , IV . 2 . 22 ( 242 ) additive

**set functions**, IV . 9 . 15**set function**. (See Continuous set ( 316 ) function and

**Set function**) Algebra , algebraic ...Page 1922

Nelson Dunford, Jacob T. Schwartz. Total space of functionals , definition , V . 3 .

1 ( 418 ) Total variation of a function , II1 . 5 . 15 ( 140 ) of a

97 ) . ( See also Variation ) Totally ordered set , 1 . 2 . 2 ( 4 ) Trace , of a finite ...

Nelson Dunford, Jacob T. Schwartz. Total space of functionals , definition , V . 3 .

1 ( 418 ) Total variation of a function , II1 . 5 . 15 ( 140 ) of a

**set function**, III . 1 . 4 (97 ) . ( See also Variation ) Totally ordered set , 1 . 2 . 2 ( 4 ) Trace , of a finite ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

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### 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 consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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