## Linear Operators, Part 1 |

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Page i

Nelson Dunford, Jacob T. Schwartz. PURE AND

Series of Texts and Monographs Edited by : R. COURANT . L. BERS J. J.

STOKER Vol . I : Supersonic Flow and Shock Waves By R. Courant and K. 0.

Friedrichs Vol ...

Nelson Dunford, Jacob T. Schwartz. PURE AND

**APPLIED**MATHEMATICS ASeries of Texts and Monographs Edited by : R. COURANT . L. BERS J. J.

STOKER Vol . I : Supersonic Flow and Shock Waves By R. Courant and K. 0.

Friedrichs Vol ...

Page 16

that F. ( A ) = -M / 3 , F. ( B ) = M0 / 3 ...

...

**Applying**the previous theorem , we find a function F. ( x ) defined on all of X suchthat F. ( A ) = -M / 3 , F. ( B ) = M0 / 3 ...

**applying**to the pair f1 , My the procedure**applied**to fo : Mo , and then continuing inductively , one obtains a sequence Fi , i...

Page 81

Theorems 1.11 , 1.17 , and 1.18 were proved for linear functionals on a general B

- space by Hahn [ 2 ] who

spaces . The first really general proofs of Theorems 1.11 and 1.13 were given by

...

Theorems 1.11 , 1.17 , and 1.18 were proved for linear functionals on a general B

- space by Hahn [ 2 ] who

**applied**these results to a large number of specialspaces . The first really general proofs of Theorems 1.11 and 1.13 were given by

...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero