## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 55

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 , ) = - \ o / 3 , F , ( B ) = o / 3 , -Mo / 3 F. ( x ) Mo / 3 . Let fi ( x ) = fo ( x ) ...

sup ( x ) ] . where Mi TEA By

**Applying**the previous theorem , we find a function F. ( x ) defined on all of X suchthat F , ( A , ) = - \ o / 3 , F , ( B ) = o / 3 , -Mo / 3 F. ( x ) Mo / 3 . Let fi ( x ) = fo ( x ) ...

sup ( x ) ] . where Mi TEA By

**applying**to the pair fully the procedure**applied**to to .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

...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero