## Linear Operators: General theory |

### From inside the book

Results 1-3 of 81

Page 48

The first occurrence of a maximum principle

principle ( as in Theorem 2 . 6 ) is in Hausdorff ( 1 ; p . 140 ] . Zorn [ 1 ] gave a

theorem essentially

...

The first occurrence of a maximum principle

**equivalent**to the well - orderingprinciple ( as in Theorem 2 . 6 ) is in Hausdorff ( 1 ; p . 140 ] . Zorn [ 1 ] gave a

theorem essentially

**equivalent**to Theorem 2 . 7 . A similar theorem is due to R . L...

Page 91

admits an

invariant metric and is complete under each invariant metric . Thus every

complete linear metric space can be metrized to be an F - space . Further , a

normed linear ...

admits an

**equivalent**metric under which it is complete , then G admits aninvariant metric and is complete under each invariant metric . Thus every

complete linear metric space can be metrized to be an F - space . Further , a

normed linear ...

Page 347

( b ) Show that L ( S , E , p ) is

countable collection of atoms of finite measure { En } in such that every

measurable subset of S - E is either an atom of infinite measure or a null set . 50

Show that no space ...

( b ) Show that L ( S , E , p ) is

**equivalent**to l , if and only if there exists acountable collection of atoms of finite measure { En } in such that every

measurable subset of S - E is either an atom of infinite measure or a null set . 50

Show that no space ...

### 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