## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 879

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

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

**contains**a normal operator T , its adjoint T * , and the identity I is a commutative B * -algebra . Thus we may state the following corollary . 15 COROLLARY .Page 995

1 and h vanishing on an open set

1 and h vanishing on an open set

**containing**the remainder of ol * ) . It follows from Lemma 12 that the set ( h * f * ° )**contains**at most the single point mo and hence , from Theorem 16 and Lemma 3.1 ( d ) , that there is a number a ...Page 996

From Lemma 12 ( b ) it is seen that olf * 9 ) Cole ) and from Lemma 12 ( c ) and the equation of = Tf it follows that o ( f * Q )

From Lemma 12 ( b ) it is seen that olf * 9 ) Cole ) and from Lemma 12 ( c ) and the equation of = Tf it follows that o ( f * Q )

**contains**no interior point of o ( 9 ) . Hence o ( f * 9 ) is a closed subset of the boundary of o ( q ) .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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