## 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

...

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 0 and if a...

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

y ) , h ...

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 ) , 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 | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 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 Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently constant contains converges convex Corollary defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math mean measure space metric neighborhood norm positive measure problem Proc projection PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero