## Linear Operators, Part 2 |

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Page 860

A B -

a B -

* + y * , ( xy ) * = y * r * ( ax ) * = ax * , ( * * ) * = x . All of the examples mentioned ...

A B -

**algebra**X is commutative in case xy = yx for all x and y in X . An involution ina B -

**algebra**X is a mapping x + x * of X into itself with the properties ( x + y ) * = ** + y * , ( xy ) * = y * r * ( ax ) * = ax * , ( * * ) * = x . All of the examples mentioned ...

Page 868

Commutative B - Algebras In case X is a commutative B -

two - sided and the quotient

be a B -

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 -

**algebra**if I is closed ( 1 . 13 ) . It is readily seen that every ideal s in X ...Page 979

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

Hilbert space L2 ( 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 L2 ( 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 | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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