## Linear Operators: Spectral theory |

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Page 860

... commutative algebra with an involution defined by f * ( 8 ) = | ( - s ) . It fails to be

a B - algebra because it lacks a

adjoined to such an algebra so that the extended algebra is a B - algebra . Let X

be an ...

... commutative algebra with an involution defined by f * ( 8 ) = | ( - s ) . It fails to be

a B - algebra because it lacks a

**unit**e . We shall show how a**unit**may beadjoined to such an algebra so that the extended algebra is a B - algebra . Let X

be an ...

Page 865

The following lemma shows that the opposite inclusion holds in case X , has the

same

whose

is ...

The following lemma shows that the opposite inclusion holds in case X , has the

same

**unit**as X . 9 LEMMA . Let æ be an element of a B - subalgebra X , of Xwhose

**unit**is the same as that of X . Then o ( x ) 0 ( x ) while the boundary of 0 , ( )is ...

Page 979

The algebra T ( L1 ( R ) ) does not contain the

closure T ( Ly ( R ) ) in the uniform operator topology contain the

algebra A is , by definition , the B - algebra obtained by adjoining the

( R ) ) .

The algebra T ( L1 ( R ) ) does not contain the

**unit**I in B ( L2 ( R ) ) nor does itsclosure T ( Ly ( R ) ) in the uniform operator topology contain the

**unit**. Thealgebra A is , by definition , the B - algebra obtained by adjoining the

**unit**I to T ( L( R ) ) .

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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