## 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 1945

This theorem and other special properties of spectral operators in

This theorem and other special properties of spectral operators in

**Hilbert space**are discussed in this section . 1 LEMMA . Let G be a bounded Abelian group of operators in**Hilbert space**H. Then there is a bounded self adjoint operator B ...Page 1947

Let B1 , ... , Bx be a finite collection of commuting bounded B. Boolean algebras of projections in a

Let B1 , ... , Bx be a finite collection of commuting bounded B. 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 ...Page 2528

Finite dimensional perturbations in Banach spaces . Amer . J. Math . ... Weak limits of powers of a contraction in

Finite dimensional perturbations in Banach spaces . Amer . J. Math . ... Weak limits of powers of a contraction in

**Hilbert space**. Proc . Amer . Math . Soc . ... On spectrality criterion for operators on a direct sum of**Hilbert spaces**.### 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 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