## Linear Operators: General theory |

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Page 224

Functions of a

Functions of a

**Complex**Variable In some of the chapters to follow , and especially 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 the ...Page 238

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

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 , addition and multiplication are understood to be defined in the natural way ...Page 274

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

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 ) ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

91 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian 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