## 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 I is a ring as well as a vector space over and if a ( wy ) ( ory = X ( ay ) , α , με Χ ...Page 44

On the other hand , if B is a Boolean ring with unit denoted by 1 , then if x = y is defined to mean x = xy , and x ' = lta then B is a Boolean

On the other hand , if B is a Boolean ring with unit denoted by 1 , then if x = y is defined to mean x = xy , and x ' = lta then B is a Boolean

**algebra**and ...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 ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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### 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