## 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 ( wy ) = ( ar y = x ( ay ) , α , με Χ , αε Φ . A right ( left , two - sided ) ideal in an**algebra**is a right ...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 ( 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