## 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

Bounded Spectral Operators in

Bounded Spectral Operators in

**Hilbert Space**What is the relationship between the bounded spectral operators in a**Hilbert space**H and the bounded normal operators in H ? The central result in this ...Page 2169

Self Adjoint Operators in

Self Adjoint Operators in

**Hilbert Space**It is the purpose of this section to show how the theory of spectral operators may be applied to yield the classical spectral theorem in**Hilbert space**, that is , the theorem asserting that a ...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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### Common terms and phrases

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 discrete domain elements equation equivalent established exists extension fact finite follows formal formula function 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