## Linear Operators: General theory |

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Page 14

... fg is

... fg is

**continuous**. The term scalar will be used for a real or complex number ; a scalar**function**is a real or complex valued**function**. ... Letf , g be**continuous**scalar**functions**on a topological space X , and let o be a scalar .Page 274

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

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 ( 8 ) ...Page 381

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

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

**continuous functions**on a locally compact Hausdorff space which vanish outside of compact sets . Arens [ 3 ] discussed certain sub - algebras of continuous ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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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