## Linear Operators: General theory |

### From inside the book

Results 1-3 of 58

Page 40

If Ø is a field , then a set X is said to be an

If Ø is a field , then a set X is said to be an

**algebra**over Ø if X is a ring as well as a vector space over Ø and if a ( wy ) = ( ar y = x ( ay ) , X , y eX , aed . A right ( left , two - sided ) ideal in an**algebra**is a right ( left ...Page 44

Thus the concepts of Boolean

Thus the concepts of Boolean

**algebra**and Boolean ring with unit are equivalent . If B and C are Boolean algebras and h : B → C , then h is said to be a homomorphism , or a Boolean**algebra**homomorphism , if h ( x ^ y ) = h ( x ) ^ h ( y ) ...Page 274

Let S be a compact Hausdorff space and C ( S ) be the

Let S be a compact Hausdorff space and C ( S ) be the

**algebra**of all complex continuous functions on S. Let A be a closed subalgebra of C ( S ) which contains the unit e and contains , with f , its complex conjugate f defined by f ( s ) ...### 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 | |

87 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 complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero