## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 89

Page 14

... g is

scalar

scalar

... g is

**continuOUS**. The term scalar will be used for a real or complex number ; ascalar

**function**is a real or complex valued**function**. ... Let f , g be**continuous**scalar

**functions**on a topological space X , and let a be a scalar . Then the**functions**...Page 274

Let S be a compact Hausdorff space and C ( S ) be the algebra of all complex

the unit e and contains , with f , its complex conjugate f defined by f ( s ) = | ( s ) .

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 containsthe unit e and contains , with f , its complex conjugate f defined by f ( s ) = | ( s ) .

Page 381

10 ) , Hewitt [ 3 ] and Edwards [ 1 ] consider functionals on the space of

of compact sets . Arens [ 3 ] discussed certain sub - algebras of

10 ) , Hewitt [ 3 ] and Edwards [ 1 ] consider functionals on the space of

**continuous functions**on a locally compact Hausdorff space which vanish outsideof compact sets . Arens [ 3 ] discussed certain sub - algebras of

**continuous****functions**on a ...### 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