## Linear Operators: Spectral theory |

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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

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 ( 1 * g ) ( x ) = / ( x y ) g ( y )

dy , ge ...

One of these algebras , namely the

**algebra**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 ( 1 * g ) ( x ) = / ( x y ) g ( y )

dy , ge ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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