## Linear Operators: General theory |

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Page 40

If x is regular , its unique inverse is denoted by r - 1 . An element which is not (

right , left ) regular is called ( right , left ) singular . If Ø is a field , then a set X is

said to be an

wy ) ...

If x is regular , its unique inverse is denoted by r - 1 . An element which is not (

right , left ) regular is called ( right , left ) singular . If Ø is a field , then a set X is

said to be an

**algebra**over Ø if I is a ring as well as a vector space over and if a (wy ) ...

Page 44

Thus the concepts of Boolean

If B and C are Boolean algebras and h : B → C , then h is said to be a

homomorphism , or a Boolean

) , h ( x vy ) ...

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 ( хлу ) = h ( x ) ^ h ( y) , h ( x vy ) ...

Page 274

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

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 ) = f ( s ) .

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

**algebra**of all complexcontinuous 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 ) = f ( s ) .

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero