## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 10

Page 376

13 13 . 14 13 . 43 13 . 43 13 . 40 Weak Convergence to x 6 . 4 , 6 . 12 , 6 . 31 13 .

13 13 . 14 6 . 31 6 . 31 Y Convergence in X = Y *

meaningless 13 . 13 13 . 14 Miscellaneous Properties 13 . 14 13 . 13 ( F4 ) 6 .

13 13 . 14 13 . 43 13 . 43 13 . 40 Weak Convergence to x 6 . 4 , 6 . 12 , 6 . 31 13 .

13 13 . 14 6 . 31 6 . 31 Y Convergence in X = Y *

**meaning**- less**meaning**- lessmeaningless 13 . 13 13 . 14 Miscellaneous Properties 13 . 14 13 . 13 ( F4 ) 6 .

Page 379

5 Conjugate Space X *

37

no 13 . 38 yes 4 . 6

5 Conjugate Space X *

**meaning**- meaningless less ( F7 ) Weak no yes no 13 .37

**meaning**| meaningless Completeness 13 . 38 4 . 7 less Reflexivity no 13 . 37no 13 . 38 yes 4 . 6

**meaning**less meaningless 13 . 37 13 . 39 13 . 45 11 . 1 13 .Page 534

L . ( S , E , u ) has a known

how to define L . ( S , E , u ) . For 1 Eps 00 , L , is a B - space , but for 0 < p < 1 , L ,

is merely an F - space ( cf . Exercise III . 9 . 30 , where , however , the symbol ...

L . ( S , E , u ) has a known

**meaning**; in the course of this section we will also seehow to define L . ( S , E , u ) . For 1 Eps 00 , L , is a B - space , but for 0 < p < 1 , L ,

is merely an F - space ( cf . Exercise III . 9 . 30 , where , however , the symbol ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 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

Akad 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 isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric 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