## 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 1947

Let B1 , ... , Bk be a finite collection of commuting

Let B1 , ... , Bk be a finite collection of commuting

**bounded**Boolean algebras of projections in a Hilbert space H. Then there exists a**bounded**self adjoint operator B in H with a**bounded**everywhere defined inverse such that BEB - 1 is ...Page 2239

X = Since f xe is a

X = Since f xe is a

**bounded**function , the operator T ( f Xe ) is a**bounded**operator . Xe If x is in E ( @ ) X as well as in E ( e ) X , it follows from the operational calculus for**bounded**functions ( cf. XVII.2.10 ) that T ( fxe ) x ...Page 2361

Let U , be a sequence of

Let U , be a sequence of

**bounded**domains covering the whole complex plane , and suppose that limi- . minze 01 121 = 0. Let Vi be the boundary of Ud . Let 0 Sv < l , and put Mi lulla - ul - 1 max λενε . μεσ ( Τ ) Let do € o ( T ) ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

31 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 contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear 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