## Linear Operators: Spectral operators |

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Page 2068

The operator algebra A ,

The operator algebra A ,

**contains**all inverses . There are a number of immediate corollaries to this theorem of Wiener which will become apparent from the following lemma . 6 LEMMA . Let J be an ideal in the subalgebra A. of A and let A ...Page 2069

Let A , be a subalgebra of A which

Let A , be a subalgebra of A which

**contains**all inverses . Then Ap**contains**all inverses . PROOF . If the operator A in Ay has an inverse in B ( HP ) then , by Corollary 9.6 , A - 1 is in AP and the determinant 8 = det ( ay ) has an ...Page 2159

1.6.9 ) , one of the sets Yn

1.6.9 ) , one of the sets Yn

**contains**a non - trivial subinterval of y . Q.E.D. 12 LEMMA ( G ) . If the point spectrum of the adjoint T ***contains**no non - trivial subarc of To , then the set of points regular relative to T is dense in ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1931 |

Copyright | |

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