## Linear Operators: General theory |

### From inside the book

Results 1-3 of 49

Page 36

It follows readily from Theorem 2.7 that in every linear vector space X there is a maximal linearly independent set B. A subset B of the linear space X is called a Hamel

It follows readily from Theorem 2.7 that in every linear vector space X there is a maximal linearly independent set B. A subset B of the linear space X is called a Hamel

**basis**or a Hamel base for X if every vector x in X has a unique ...Page 71

A sequence { Xn } in an F - space X is called a

A sequence { Xn } in an F - space X is called a

**basis**for X if to each xe X there corresponds a unique sequence { Q } of scalars such that lim ( 2 – 3 arti ! 0 . n n - 00 8 Let ( wn } be a**basis**in the F - space X , and let y be the ...Page 254

Thus by forming the chain UB , UM , ... , Uz ' , Vz . it is seen that vp is equivalent to vg , and thus that Vp is in V. Since { vp } is a

Thus by forming the chain UB , UM , ... , Uz ' , Vz . it is seen that vp is equivalent to vg , and thus that Vp is in V. Since { vp } is a

**basis**, the vector u , has an expansion of the form un = E ( ux , VB ) 0g , so that u , is in the ...### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

91 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero