## Linear Operators, Part 1 |

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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 , its

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 ) which

contains the unit e and contains , with , its

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

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 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

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