## Linear Operators: General theory |

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Page 14

X, Y, Z are topological spaces, and if f : X -+Y and g : Y -+ Z are

the composite

complex number; a scalar

X, Y, Z are topological spaces, and if f : X -+Y and g : Y -+ Z are

**continuous**, thenthe composite

**function**fg is**continuous**. The term scalar will be used for a real orcomplex number; a scalar

**function**is a real or complex valued**function**.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) = /(*). Then

2t ...

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

**continuous functions**on S. Let 21 be a closed subalgebra of C(S) which containsthe unit e and contains, with f, its complex conjugate f defined by f(s) = /(*). Then

2t ...

Page 381

10], Hewitt [3] and Edwards [1] consider functionals on the space of

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 outside of compactsets. 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 | |

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### 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

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero