## Linear Operators: Spectral theory |

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Page 877

Then an

Consequently the spectrum of y as an

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 asan

**element**of X . Proof . If y - 1 exists as an**element**of Y then , since X and Y ...Page 878

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

determines the * - isomorphism uniquely and we are thus led to the following

definition . 12 DEFINITION . Let x be an

and let fe C ...

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 * - algebraand let fe C ...

Page 1339

An

The set of all equivalence classes of

functions will be denoted by L2 ( { uis } ) . We observe that by Lemma 7 , the ...

An

**element**F of Ly ( { Mij } ) will be said to be a { Miss - null function if | F | = 0 .The set of all equivalence classes of

**elements**of Ly ( { uis } ) modulo { u ; } - nullfunctions will be denoted by L2 ( { uis } ) . We observe that by Lemma 7 , the ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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