## Linear Operators: Spectral operators |

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Results 1-3 of 93

Page 2068

The operator algebra A ,

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 ( I ) ...

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 lemma . ; 6 LEMMA . Let J be an ideal in the subalgebra A . of A and let

A ( I ) ...

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

9 ) , one of the sets Yn

LEMMA ( G ) . If the point spectrum of the adjoint 7 *

subarc of To , then the set of points regular relative to T is dense in To . PROOF .

If X is not ...

9 ) , one of the sets Yn

**contains**a non - trivial subinterval of y . Q . E . D . 12LEMMA ( G ) . If the point spectrum of the adjoint 7 *

**contains**no non - trivialsubarc of To , then the set of points regular relative to T is dense in To . PROOF .

If X is not ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 other sections not shown

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