## Linear operators: Spectral operators |

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Results 1-3 of 86

Page 2068

The operator algebra 21 i

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

following lemma. 6 Lemma. Let 3 be an ideal in the subalgebra 2I0 of 21 and let

21(3) ...

The operator algebra 21 i

**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 3 be an ideal in the subalgebra 2I0 of 21 and let

21(3) ...

Page 2069

Let 9I0 be a svbalgebra of 91 which

inverses. Proof, If the operator A in 9lg has an inverse in £(§") then, by Corollary

9.6, A ~ 1 is in SI" and the determinant 8 = det(a(/) has an inverse in 91. Since 9t0

...

Let 9I0 be a svbalgebra of 91 which

**contains**all inverses. Then 9lg**contains**allinverses. Proof, If the operator A in 9lg has an inverse in £(§") then, by Corollary

9.6, A ~ 1 is in SI" and the determinant 8 = det(a(/) has an inverse in 91. Since 9t0

...

Page 2286

resolution of the identity E(-) of Q and suppose that B

infinite uniform multiplicity. If A is the closed densely defined linear map of X into

the Hilbert space § of Lemma 35, then the closure Q of AQA ~ 1 is a bounded ...

resolution of the identity E(-) of Q and suppose that B

**contains**no projection ofinfinite uniform multiplicity. If A is the closed densely defined linear map of X into

the Hilbert space § of Lemma 35, then the closure Q of AQA ~ 1 is a bounded ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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