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

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero