## Linear Operators: General theory |

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Page 168

Let ( S , E , u ) be a positive measure space and G a

, M , X ) , where 1 sp < 0o . Then there is a set S , in £ , a sub o - field £ of E ( S ) ,

and a closed

...

Let ( S , E , u ) be a positive measure space and G a

**separable**subset of L ( S , E, M , X ) , where 1 sp < 0o . Then there is a set S , in £ , a sub o - field £ of E ( S ) ,

and a closed

**separable**subspace X of X such that the restriction M of u to £ , has...

Page 507

may be noted that the next theorem applies to every continuous linear map of L (

S , E , u ) into a

finite positive measure space , and let T be a weakly compact operator on L ( S ...

may be noted that the next theorem applies to every continuous linear map of L (

S , E , u ) into a

**separable**reflexive space . 10 THEOREM . Let ( S , E , u ) be a o -finite positive measure space , and let T be a weakly compact operator on L ( S ...

Page 854

... V.7.14 ( 436 )

1.6.11 ( 21 ) . ( See also

, II.1.5 ( 50 ) . in reflexive spaces , 11.3.28 ( 68 ) in special spaces , IV.15 Series .

... V.7.14 ( 436 )

**Separability**and metrizability , V.5.1-2 ( 426 )**Separable**sets ,1.6.11 ( 21 ) . ( See also

**Separable**linear manifolds )**Separable**linear manifolds, II.1.5 ( 50 ) . in reflexive spaces , 11.3.28 ( 68 ) in special spaces , IV.15 Series .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero