## Linear Operators, Part 2 |

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Page 879

It is clear that the smallest closed subalgebra of B ( H ) which

operator T , its adjoint T * , and the identity I is a commutative B * - algebra . Thus

we may state the following corollary . 15 COROLLARY . Let T be a normal ...

It is clear that the smallest closed subalgebra of B ( H ) which

**contains**a normaloperator T , its adjoint T * , and the identity I is a commutative B * - algebra . Thus

we may state the following corollary . 15 COROLLARY . Let T be a normal ...

Page 995

Let h be in L ( R ) with himo ) = 1 and h vanishing on an open set

remainder of olf * ° ) . It follows from Lemma 12 that the set ( h * f * )

most the single point me and hence , from Theorem 16 and Lemma 3 . 1 ( d ) ,

that ...

Let h be in L ( R ) with himo ) = 1 and h vanishing on an open set

**containing**theremainder of olf * ° ) . It follows from Lemma 12 that the set ( h * f * )

**contains**atmost the single point me and hence , from Theorem 16 and Lemma 3 . 1 ( d ) ,

that ...

Page 996

From Lemma 12 ( b ) it is seen that olf * 9 ) Colg ) and from Lemma 12 ( c ) and

the equation of = tf it follows that olf * Q )

Hence o ( f * 9 ) is a closed subset of the boundary of o ( a ) . Since f * 9 = 0 it

follows ...

From Lemma 12 ( b ) it is seen that olf * 9 ) Colg ) and from Lemma 12 ( c ) and

the equation of = tf it follows that olf * Q )

**contains**no interior point of o ( 9 ) .Hence o ( f * 9 ) is a closed subset of the boundary of o ( a ) . Since f * 9 = 0 it

follows ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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