## Linear Operators, Part 1 |

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Results 1-3 of 10

Page 326

Let Ox and nx have the same

fr is u - integrable it follows from Egoroff's theorem ( III.6.12 ) and the second

paragraph of the proof of Theorem III.2.22 that there is a simple function gk and a

set ...

Let Ox and nx have the same

**meaning**as in the previous paragraph . Since eachfr is u - integrable it follows from Egoroff's theorem ( III.6.12 ) and the second

paragraph of the proof of Theorem III.2.22 that there is a simple function gk and a

set ...

Page 379

... Sequences meaningless meaningless 13.37 13.41 13.4 Weak Convergence to

x meaningless meaningless 13.44 Y Convergence in X = Y * meaningless

XI.2 ...

... Sequences meaningless meaningless 13.37 13.41 13.4 Weak Convergence to

x meaningless meaningless 13.44 Y Convergence in X = Y * meaningless

**meaning**.. less meaningless meaningless Miscellaneous Properties 7.6 SectionXI.2 ...

Page 534

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

how to define L ( S , E , u ) . For 1 < p soo , 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 I , has

...

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 < p soo , 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 I , has

...

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### 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