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

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Page 877

Then an

Then an

**element**y in Y has an inverse in X if and only if it has an inverse in Y. Consequently the spectrum of y as an**element**of Y is the same as its spectrum as an**element**of X. Proof . If y - l exists as an**element**of Y then , since ...Page 878

Clearly the requirement that x and g ( u ) = u be corresponding

Clearly the requirement that x and g ( u ) = u be corresponding

**elements**determines the * -isomorphism uniquely and we are thus led to the following definition . 12 DEFINITION . Let x be an**element**of a commutative B * -algebra and let ...Page 1339

An

An

**element**F of L ? ( { ui ; } ) will be said to be a { Mis } -null function if ( F ] = 0. The set of all equivalence classes of**elements**of L ? ( { u is } ) modulo { u is } -null functions will be denoted by L2 ( { uis } ) .### 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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