## Linear Operators: General theory |

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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 ...Page 838

space of, definition, IV.2.24 (242) properties, IV.15 Annihilator of a set, II.4.17 (72)

Arzela theorem, on continuity of limit function, IV.6.11 (268) remarks concerning, (

883) Ascoli-Arzela theorem, on compactness of

space of, definition, IV.2.24 (242) properties, IV.15 Annihilator of a set, II.4.17 (72)

Arzela theorem, on continuity of limit function, IV.6.11 (268) remarks concerning, (

883) Ascoli-Arzela theorem, on compactness of

**continuous functions**, IV.6.7 ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional 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 neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero