## 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**. ... Let f , 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 ( s ) ...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 [ 8 ] 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 |

Algebraic Preliminaries | 34 |

Copyright | |

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