## Linear Operators, Part 2 |

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Page 868

If I is a closed ideal in the commutative B - algebra X then the quotient algebra X /

I is isometrically isomorphic to the

maximal . PROOF . If I is not maximal it is properly contained in an ideal and so X

/ 3 ...

If I is a closed ideal in the commutative B - algebra X then the quotient algebra X /

I is isometrically isomorphic to the

**field**of complex numbers if and only if I ismaximal . PROOF . If I is not maximal it is properly contained in an ideal and so X

/ 3 ...

Page 1048

... w ] + x = rw is evidently a homeomorphism of RXS onto E " . Thus the o -

, of Borel subsets of EM is the product o -

of R and the o -

... w ] + x = rw is evidently a homeomorphism of RXS onto E " . Thus the o -

**field**B, of Borel subsets of EM is the product o -

**field**of the o -**field**BR of Borel subsetsof R and the o -

**field**Bs of Borel subsets of S , in the sense of Definition III . 11 .Page 1153

Thus the product group has a Haar measure 2 ( 2 ) defined on its Borel

. It is natural to expect that the product measure à xa coincides , up to a constant

multiple , with 2 ( 2 ) . This fact will be established in Theorem 7 . 6 LEMMA .

Thus the product group has a Haar measure 2 ( 2 ) defined on its Borel

**field**{ ( 2 ). It is natural to expect that the product measure à xa coincides , up to a constant

multiple , with 2 ( 2 ) . This fact will be established in Theorem 7 . 6 LEMMA .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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