## Linear Operators: Spectral theory |

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Page 868

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 2 .

two - sided and the quotient algebra X / I is again a

be a B ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 2 .

**Commutative**B - Algebras In case X is a**commutative**B - algebra every ideal I istwo - sided and the quotient algebra X / I is again a

**commutative**algebra . It willbe a B ...

Page 869

Every homomorphism of a

system is continuous . 4 LEMMA . Let M be the set of maximal ideals in the

.

Every homomorphism of a

**commutative**B - algebra into the complex numbersystem is continuous . 4 LEMMA . Let M be the set of maximal ideals in the

**commutative**B - algebra X . Then x ( M ) = Q ( x ) and sup \ X ( M ) ] = lim ( x " | 1 / ".

Page 882

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. where E is

an arbitrary Borel subset of R , and E , = { ( x , y ) € RXR lac + ye E } . Show that

with the product u * 2 the Banach space M is a

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. where E is

an arbitrary Borel subset of R , and E , = { ( x , y ) € RXR lac + ye E } . Show that

with the product u * 2 the Banach space M is a

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

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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