## Linear Operators: Spectral theory |

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Page 860

A B - algebra X is commutative in case xy = yæ for all x and y in X . An involution

in a

and the class of analytic functions , are commutative

.

A B - algebra X is commutative in case xy = yæ for all x and y in X . An involution

in a

**B**-**algebra**X is a mapping x → * * of X ... with the exception of L ( - 00 , 0 )and the class of analytic functions , are commutative

**B**-**algebras**with involutions.

Page 861

given algebra X is algebraically and topologically equivalent to the

X ) . Since \ Q1 = | xel = \ Tzel = lel | Tel it follows that the inverse map r 1 is

continuous . To see that t is also continuous it will first be shown that t ( X ) is

closed ...

given algebra X is algebraically and topologically equivalent to the

**B**-**algebra**T (X ) . Since \ Q1 = | xel = \ Tzel = lel | Tel it follows that the inverse map r 1 is

continuous . To see that t is also continuous it will first be shown that t ( X ) is

closed ...

Page 868

Nelson Dunford, Jacob T. Schwartz. 2 . Commutative

commutative

is again a commutative algebra . It will be a

Nelson Dunford, Jacob T. Schwartz. 2 . Commutative

**B**-**Algebras**In case X is acommutative

**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 ) .### What people are saying - Write a review

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

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