## Linear Operators: General theory |

### From inside the book

Results 1-3 of 9

Page 326

Let 8x and nx have the same

fx 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 8x and nx have the same

**meaning**as in the previous paragraph . Since eachfx 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 376

Weakly Compact Sets 13.13 13.14 6.29 6.29 6.14 Weak Cauchy Sequences

13.13 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

meaningless ...

Weakly Compact Sets 13.13 13.14 6.29 6.29 6.14 Weak Cauchy Sequences

13.13 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

**meaning**. lessmeaningless ...

Page 379

TM ( S ,, u ) 28. s ( F9 ) 4.5 Conjugate Space ** meaningless meaningless ( F7 )

no Weak Completeness no 13.38 yes 4.7 meaningless

Reflexivity no 13.37 no 13.38 yes 4.6 meaningless meaningless 13.37 13.39

13.45 ...

TM ( S ,, u ) 28. s ( F9 ) 4.5 Conjugate Space ** meaningless meaningless ( F7 )

no Weak Completeness no 13.38 yes 4.7 meaningless

**meaning**. less 13.37Reflexivity no 13.37 no 13.38 yes 4.6 meaningless meaningless 13.37 13.39

13.45 ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero