## Linear Operators: General theory |

### From inside the book

Results 1-3 of 54

Page 40

If x is regular , its unique yx . 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 yx . 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 I is a ring as well ...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 ) Ah ( 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

User Review - Flag as inappropriate

i want to read

### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

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