## Linear Operators: Spectral operators |

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Page 2068

Thus Wiener's result may be stated as follows . 5 COROLLARY ( N. Wiener ) .

The operator algebra A ,

corollaries to this theorem of Wiener which will become apparent from the

following ...

Thus Wiener's result may be stated as follows . 5 COROLLARY ( N. Wiener ) .

The operator algebra A ,

**contains**all inverses . There are a number of immediatecorollaries to this theorem of Wiener which will become apparent from the

following ...

Page 2069

Let A , be a subalgebra of A which

inverses . PROOF . If the operator A in Ag has an inverse in B ( HP ) then , by

Corollary 9.6 , A - 1 is in AP and the determinant S = det ( ay ) has an inverse in A

.

Let A , be a subalgebra of A which

**contains**all inverses . Then Ap**contains**allinverses . PROOF . If the operator A in Ag has an inverse in B ( HP ) then , by

Corollary 9.6 , A - 1 is in AP and the determinant S = det ( ay ) has an inverse in A

.

Page 2159

1.6.9 ) , one of the sets yn

LEMMA ( G ) . If the point spectrum of the adjoint T *

subarc of T ' , then the set of points regular relative to T is dense in To PROOF . If

X is not in ...

1.6.9 ) , one of the sets yn

**contains**a non - trivial subinterval of gi Q.E.D. 12LEMMA ( G ) . If the point spectrum of the adjoint T *

**contains**no non - trivialsubarc of T ' , then the set of points regular relative to T is dense in To PROOF . If

X is not in ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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