## Linear Operators: General theory |

### From inside the book

Results 1-3 of 62

Page 168

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

, M , X ) , where 1 sp < 00 . Then there is a set S , in E , a sub o - field Ey 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 < 00 . Then there is a set S , in E , a sub o - field Ey of E ( S ) ,

and a closed

**separable**subspace X of % such that the restriction My of u to Ey ...Page 501

If the compact Hausdorff space S has a countable base the space C ( S ) is

space . If y ( x , y ) is a metric in S let 1n ( x ) = Q ( x , xn ) where { Xn } is a

denumerable ...

If the compact Hausdorff space S has a countable base the space C ( S ) is

**separable**. Proof . By Theorems 1 . 6 . 19 and 1 . 6 . 12 , S is a**separable**metricspace . If y ( x , y ) is a metric in S let 1n ( x ) = Q ( x , xn ) where { Xn } is a

denumerable ...

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 ...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

5 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group 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