## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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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 I be an ideal in the subalgebra A , of A and let ...Page 2069

Let A , be a subalgebra of A which

Let A , be a subalgebra of A which

**contains**all inverses . Then Ag**contains**all inverses . PROOF . If the operator A in A has an inverse in B ( HP ) then , by Corollary 9.6 , A - 1 is in AP and the determinant S = det ( ay ) has an ...Page 2286

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

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

**contains**no projection of infinite uniform multiplicity . If A is the closed densely defined linear map of X into the Hilbert space H of Lemma 35 , then the closure of AQA - 1 is ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero