## Linear Operators: General theory |

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Page 14

The term scalar will be used for a real or complex number ; a scalar

real or complex valued

scalar

The term scalar will be used for a real or complex number ; a scalar

**function**is areal or complex valued

**function**. The topology in the ... Let f , g be**continuous**scalar

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

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

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

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

= f ( 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

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### Contents

Preliminary Concepts A Settheoretic Preliminaries 1 Notation and Elementary Notions | 1 |

Partially Ordered Systems | 7 |

Exercises | 9 |

Copyright | |

35 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

algebra analytic applied arbitrary assumed B-space ba(S Borel bounded called Chapter clear closed compact complex condition Consequently constant contains continuous functions converges Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hausdorff Hence Hilbert space identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear space mapping Math means measure space neighborhood norm obtained operator positive measure preceding projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero