## Linear Operators: General theory |

### From inside the book

Results 1-3 of 91

Page 182

Thus da / du is

uds ) , Ee2 . ... field ) of sets in Sq . For an additive set function Ma on £ , the

equation 4 ( 8 - 4 ( E ) ) = M2 ( E )

Moreover ...

Thus da / du is

**defined**u - almost everywhere by the formula 2 ( E ) = S , 7 ( - )uds ) , Ee2 . ... field ) of sets in Sq . For an additive set function Ma on £ , the

equation 4 ( 8 - 4 ( E ) ) = M2 ( E )

**defines**an additive set function My on Ex .Moreover ...

Page 240

It is evident that if we

and u ( d ) = 0 ... The space B ( S ) is

all bounded scalar functions on S . The norm is given by W = sup \ | ( s ) ] . 14 .

It is evident that if we

**define**the set function u on & by placing u ( E ) = 0 if E + 6and u ( d ) = 0 ... The space B ( S ) is

**defined**for an arbitrary set S and consists ofall bounded scalar functions on S . The norm is given by W = sup \ | ( s ) ] . 14 .

Page 241

u , S ) . 18 . The space L ( S , E , u ) is

and any positive measure space ( S , E , ) . It consists of those u - measurable ...

**defined**on the o - field B of all Borel sets in S . The norm ul is the total variation v (u , S ) . 18 . The space L ( S , E , u ) is

**defined**for any real number p , 13p < 0 ,and any positive measure space ( S , E , ) . It consists of those u - measurable ...

### 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