## Linear Operators, Part 1 |

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Page 40

For if I is maximal , then RȚI is a commutative ring with

ideals ; by what we showed earlier RI is a field . Conversely , if RI is a field , it

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

with ...

For if I is maximal , then RȚI is a commutative ring with

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

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

with ...

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 RM is isomorphic with the field 02 . An important example of aBoolean ring with a

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

Page 485

Nelson Dunford, Jacob T. Schwartz. set TS . Hence Yni ? 8 THEOREM . (

Gantmacher ) An operator in B ( x , y ) is weakly compact if and only if its adjoint is

weakly compact . Proof . Let T be weakly compact . Since the closed

S * of ...

Nelson Dunford, Jacob T. Schwartz. set TS . Hence Yni ? 8 THEOREM . (

Gantmacher ) An operator in B ( x , y ) is weakly compact if and only if its adjoint is

weakly compact . Proof . Let T be weakly compact . Since the closed

**unit**sphereS * of ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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