## Linear Operators: Spectral theory |

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Page 860

A B -

a B -

* + y * , ( xy ) * = y * * * ( aux ) * = āx * , ( w * ) * = x . All of the examples ...

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 + * * of X into itself with the properties ( x + y ) * = x* + y * , ( xy ) * = y * * * ( aux ) * = āx * , ( w * ) * = x . All of the examples ...

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 I in X ...Page 979

One of these algebras , namely the

met before . For convenience , its definition and some of its properties will be

restated here . For every f in Ly ( R ) the convolution ( * g ) ( x ) = Sa + ( x y ) g ( y )

dy ...

One of these algebras , namely the

**algebra**A of the preceding section , we havemet before . For convenience , its definition and some of its properties will be

restated here . For every f in Ly ( R ) the convolution ( * g ) ( x ) = Sa + ( x y ) g ( y )

dy ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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