## Linear Operators: General theory |

### From inside the book

Results 1-3 of 86

Page 72

1.11 ) is a

1.11 ) is a

**B**-**space**( or an F -**space**) with the metric ( x + 3 ) = inf ( x + 2 !. ze3 ( Hint : Given a Cauchy sequence in X / 3 , define a subsequence ...Page 89

In the definitions of F- and

In the definitions of F- and

**B**-**spaces**, we required the**spaces**to be complete in ... Let X be a linear**space**satisfying properties ( i ) and ( ii ) of ...Page 398

168 ] showed that every X - convergent sequence in X * is actually X ** - convergent , and that if Y is a separable

168 ] showed that every X - convergent sequence in X * is actually X ** - convergent , and that if Y is a separable

**B**-**space**, then any operator in**B**( X ...### 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 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 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 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