## Linear Operators: General theory |

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Page 224

Functions of a

especially in Chapter VII , we shall use extensions of certain well - known results

in the theory of analytic functions of a

functions ...

Functions of a

**Complex**Variable In some of the chapters to follow , andespecially in Chapter VII , we shall use extensions of certain well - known results

in the theory of analytic functions of a

**complex**variable to the case where thefunctions ...

Page 238

With the one exception of Hilbert space , each of them will consist of real or

and multiplication are understood to be defined in the natural way , i . e . , by the ...

With the one exception of Hilbert space , each of them will consist of real or

**complex**valued functions f , g defined on a specified domain S . Here , additionand multiplication are understood to be defined in the natural way , i . e . , by the ...

Page 274

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

continuous functions on S . Let A be a closed subalgebra of C ( S ) which

contains the unit e and contains , with f , its

= f ( $ ) .

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 ) which

contains the unit e and contains , with f , its

**complex**conjugate f defined by F ( s )= f ( $ ) .

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 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

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