## Linear Operators, Part 2 |

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Page 891

scalar functions with respect to the operator valued set

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 1174

prove the reverse inequality for a dense subset of L , ( X ) , so that we may

assume without loss of generality that f is a simple

on each of the disjoint sets ej , i = 1 , . . . , n , and that i vanishes outside the union

of ...

prove the reverse inequality for a dense subset of L , ( X ) , so that we may

assume without loss of generality that f is a simple

**function**, i . e . , that f ( s ) = x ;on each of the disjoint sets ej , i = 1 , . . . , n , and that i vanishes outside the union

of ...

Page 1922

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

1 ( 418 ) Total variation 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

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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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 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 give 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