## 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

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

21 ...

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

**continuous functions**on S. Let %be a closed subalgebra of C(S) which containsthe unit e and contains, with f, its complex conjugate f defined by f(s) = f(s). Then

21 ...

Page 381

10], Hewitt [8] and Edwards [1] consider functionals on the space of

sets. Arens [3] discussed certain sub-algebras of

10], Hewitt [8] and Edwards [1] consider functionals on the space of

**continuous****functions**on a locally compact Hausdorff space which vanish outside of compactsets. Arens [3] discussed certain sub-algebras of

**continuous functions**on a ...Page 841

criteria for the limit to be continuous, 1.7.7 (29), IV.6.11 (268) definition, 1.4.15 (13

) density in TM and L„, III.'.). 14 (170), IV.8.19 (298) existence of non-differentiable

criteria for the limit to be continuous, 1.7.7 (29), IV.6.11 (268) definition, 1.4.15 (13

) density in TM and L„, III.'.). 14 (170), IV.8.19 (298) existence of non-differentiable

**continuous functions**, 1.9.6 (38) existence on a normal space, 1.5.2 (15) ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

44 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

Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero