## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 865

An

idempotent with 0 # 20 #e clearly has 0. ( x ) Co ( x ) . The following lemma shows

that the opposite inclusion holds in case X , has the same unit as X. 9 LEMMA .

Let x be ...

An

**element**x in a B - subalgebra of the form Xo = e . Xe , where e , is anidempotent with 0 # 20 #e clearly has 0. ( x ) Co ( x ) . The following lemma shows

that the opposite inclusion holds in case X , has the same unit as X. 9 LEMMA .

Let x be ...

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 - l exists as an**element**of Y then , since X and Y ...Page 1339

An

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 ( { uis } ) will be said to be a { Mis } -null function if | F1 = 0. Theset of all equivalence classes of

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

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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