## 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 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

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 | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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