## Linear Operators: Spectral theory |

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**element**æ in a B - subalgebra of the form Xo = exe , where e , is an idempotent with 0 # 20 # e clearly has oo ( a ) Co ( w ) . The following lemma shows that the opposite inclusion holds in case X , has the same unit as X. 9 LEMMA .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 1339

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**element**F of L ? ( { dis } ) will be said to be a { ti ; } - null function if ( F ) = 0. The set of all equivalence classes of**elements**of L ? ( { Wix } ) modulo { ujj } -null functions will be denoted by L2 ( { u } ) .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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