## Linear Operators: Spectral theory |

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Page 860

A B-

a B-

++y”, (ay)* = y”a." (xa)* = &a", (wo)* = a. All of the examples mentioned above, ...

A B-

**algebra**3 is commutative in case a y = ya for all a and y in 3. An involution ina B-

**algebra**3 is a mapping a -> a.” of 3: into itself with the properties (a-i-y)* = a++y”, (ay)* = y”a." (xa)* = &a", (wo)* = a. All of the examples mentioned above, ...

Page 868

Commutative B-Algebras In case 3 is a commutative B-

two-sided and the quotient

a B-

Commutative B-Algebras In case 3 is a commutative B-

**algebra**every ideal & istwo-sided and the quotient

**algebra**3/3 is again a commutative**algebra**. It will bea B-

**algebra**if 3 is closed (1.18). It is readily seen that every ideal & in 3: which ...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 L1(R) the convolution ( . )(x) = s.st-w)gsu)ay, ge L2(R

), ...

One of these algebras, namely the

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

restated here. For every f in L1(R) the convolution ( . )(x) = s.st-w)gsu)ay, ge L2(R

), ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 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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