## Linear Operators: General theory |

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Page 40

If Ø is a field , then a set X is said to be an

If Ø is a field , then a set X is said to be an

**algebra**over Ø if X is a ring as well as a vector space over Ø and if a ( xy ) = ( axby = x ( ay ) , α , με Χ , αε Φ . A right ( left , two - sided ) ideal in an ...Page 44

Thus the concepts of Boolean

Thus the concepts of Boolean

**algebra**and Boolean ring with unit are equivalent . If B and C are Boolean**algebras**and h : B → C , then h is said to be a homomorphism , or a Boolean**algebra**homomorphism , if h ( x ^ y ) = h ( x ) h ( y ) ...Page 274

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

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 continuous functions 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 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