## Linear Operators: General theory |

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Page 40

If x is regular , its unique inverse is denoted by x - 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

a ...

If x is regular , its unique inverse is denoted by x - 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 X is a ring as well as a vector space over Ø and ifa ...

Page 44

Thus the concepts of Boolean

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

homomorphism , or a Boolean

y ) , h ...

Thus the concepts of Boolean

**algebra**and Boolean ring with unit are equivalent .If B and Care 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 ) , h ...

Page 272

We continue our analysis of the space C ( S ) with a discussion of certain

important special properties related to its structure as an

properties is a well known approximation theorem of Weierstrass , which asserts

that a ...

We continue our analysis of the space C ( S ) with a discussion of certain

important special properties related to its structure as an

**algebra**. One of theseproperties is a well known approximation theorem of Weierstrass , which asserts

that a ...

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### Contents

Preliminary Concepts A Settheoretic Preliminaries 1 Notation and Elementary Notions | 1 |

Partially Ordered Systems | 7 |

Exercises | 9 |

Copyright | |

35 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

algebra analytic applied arbitrary assumed B-space ba(S Borel bounded called Chapter clear closed compact complex condition Consequently constant contains continuous functions converges Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hausdorff Hence Hilbert space identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear space mapping Math means measure space neighborhood norm obtained operator positive measure preceding projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero