## Linear Operators: General theory |

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Results 1-3 of 73

Page 40

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

ideals ; by what we showed earlier R / I is a field . Conversely , if R / I is a field , it

contains no ideals and hence R has no ideals properly containing I. If R is a ring

...

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

**unit**which has no properideals ; by what we showed earlier R / I is a field . Conversely , if R / I is a field , it

contains no ideals and hence R has no ideals properly containing I. If R is a ring

...

Page 41

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

with

Boolean ring with a

be a ...

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 aBoolean ring with a

**unit**is the ring of subsets of a fixed set . More precisely , let Sbe a ...

Page 458

5 If the closed

finite number of extremal points , then X is not isometrically isomorphic to the

conjugate of any B - space . 6 Let S be a topological space , and let C ( S ) be the

B ...

5 If the closed

**unit**sphere of an infinite dimensional B - space X contains only afinite number of extremal points , then X is not isometrically isomorphic to the

conjugate of any B - space . 6 Let S be a topological space , and let C ( S ) be the

B ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero