## Linear Operators: General theory |

### From inside the book

Results 1-3 of 87

Page 88

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

separability

the Hahn - Banach theorem to hold when the field of scalars is non ...

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

**condition**is sufficient . Bonsall [ 1 ] showed that theseparability

**condition**cannot be dropped . Ingleton ( 1 ) has given**conditions**forthe Hahn - Banach theorem to hold when the field of scalars is non ...

Page 131

To prove the sufficiency of the

satisfies this

and imaginary parts satisfy the same

is ...

To prove the sufficiency of the

**condition**we observe first that a set function àsatisfies this

**condition**if and only if the positive and negative variations of its realand imaginary parts satisfy the same

**condition**. Thus , it may be assumed that ais ...

Page 487

in S. Hence , by IV.6.6 , the

an equicontinuous subset of C ( S * ) . It follows from Theorem IV.6.7 , that T ( S )

is conditionally compact in the metric of Y if and only if the

in S. Hence , by IV.6.6 , the

**condition**is equivalent to the statement that T ( S ) isan equicontinuous subset of C ( S * ) . It follows from Theorem IV.6.7 , that T ( S )

is conditionally compact in the metric of Y if and only if the

**condition**is satisfied .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume 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 domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen 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