## Linear Operators: Spectral theory |

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Page 868

Nelson Dunford, Jacob T. Schwartz. 2 . Commutative B - Algebras In case X is a

commutative B -

is again a commutative

Nelson Dunford, Jacob T. Schwartz. 2 . Commutative B - Algebras In case X is a

commutative B -

**algebra**every ideal I is two - sided and the quotient**algebra**X / Iis again a commutative

**algebra**. It will be a B -**algebra**if I is closed ( 1 . 13 ) .Page 875

2 LEMMA . The

in which the operation * of involution is defined by equation ( i ) is a B * -

Our chief objective in this section is to characterize commutative B * - algebras .

2 LEMMA . The

**algebra**B ( H ) of all bounded linear operators in Hilbert space Hin which the operation * of involution is defined by equation ( i ) is a B * -

**algebra**.Our chief objective in this section is to characterize commutative B * - algebras .

Page 979

be based upon two closely related commutative algebras of operators in the

Hilbert space L ( R ) . One of these algebras , namely the

preceding section , we have met before . For convenience , its definition and

some of its ...

be based upon two closely related commutative algebras of operators in the

Hilbert space L ( R ) . One of these algebras , namely the

**algebra**A of thepreceding section , we have met before . For convenience , its definition and

some of its ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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