## 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 1917

If an unperturbed operator T and a perturbed operator T ” derived from it are both

self adjoint , then a non - rigorous

expectation that the Friedrichs operator U realizing the similarity UTU - 1 = T ...

If an unperturbed operator T and a perturbed operator T ” derived from it are both

self adjoint , then a non - rigorous

**formal**argument can be used to buttress theexpectation that the Friedrichs operator U realizing the similarity UTU - 1 = T ...

Page 2020

We may therefore conclude from Theorem 7 that the natural closed extension As

of the

whole complex plane unless A is of order zero , that is , none of its elements ...

We may therefore conclude from Theorem 7 that the natural closed extension As

of the

**formal**differential operator ( 18 ) with An P = 0 has its spectrum o ( As ) thewhole complex plane unless A is of order zero , that is , none of its elements ...

Page 2371

... who studied the case in which linear conditions are imposed at interior points

of the interval of definition of a

theoretic approach via perturbation theorems used in Section 2 was introduced ...

... who studied the case in which linear conditions are imposed at interior points

of the interval of definition of a

**formal**differential operator . The abstract operator -theoretic approach via perturbation theorems used in Section 2 was introduced ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero