## Linear Operators: General theory |

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Page 40

For if I is maximal , then R ] I is a commutative ring with

For if I is maximal , then R ] I is a commutative ring with

**unit**which has no proper ideals ; by what we showed earlier RI is a field .Page 41

Further , from the above we see that if M is a maximal ideal in a Boolean ring R with

Further , from the above we see that if M is a maximal ideal in a Boolean ring R with

**unit**, then R / M is isomorphic with the field An important example of ...Page 425

The X * -closure of x ( X ) is a subspace of X ** , which , by Theorem 5 , contains the

The X * -closure of x ( X ) is a subspace of X ** , which , by Theorem 5 , contains the

**unit**sphere of X ** . It follows immediately that it contains every ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

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