## Linear Operators: General theory |

### From inside the book

Results 1-3 of 84

Page 88

x = p ( x ) + p ( -x ) , then this

x = p ( x ) + p ( -x ) , then this

**condition**is sufficient . Bonsall [ 1 ] showed that the separability**condition**cannot be dropped . Ingleton [ 1 ] has given**conditions**for the Hahn - Banach theorem to hold when the field of scalars is ...Page 131

To prove the sufficiency of the

To prove the sufficiency of the

**condition**we observe first that a set function 2 satisfies this**condition**if and only if the positive and negative variations of its real and imaginary parts satisfy the same**condition**.Page 433

The necessity of the

The necessity of the

**condition**is immediate from 1.5.6 . For the sufficiency , we observe that the**condition**implies that K is bounded . For otherwise , there exists an a * EX * such that x * ( K ) is an unbounded convex set of scalars ...### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 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 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