## 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 1915

... whose primary interest is in the applications to such topics as scattering theory

, the quantum mechanical version of the three body problem , and other

contemporary problems of mathematical physics to which the results of Chapter

XX

... whose primary interest is in the applications to such topics as scattering theory

, the quantum mechanical version of the three body problem , and other

contemporary problems of mathematical physics to which the results of Chapter

XX

**apply**...Page 2409

We may therefore

sufficiently small , then the operator T and the operator T + 9 ( A ) are similar .

Since T is obviously a spectral operator of scalar type , T + ( A ) must also be a

spectral ...

We may therefore

**apply**Theorem 1 , to find that if A € A , and if | | A | | issufficiently small , then the operator T and the operator T + 9 ( A ) are similar .

Since T is obviously a spectral operator of scalar type , T + ( A ) must also be a

spectral ...

Page 2434

D . By using appropriate “ diagonalizing ” transformations ( cf . Theorem XII . 3 .

16 ) , we may

...

**Applying**Theorem 8 and Corollary 9 , the present theorem follows at once . Q . E .D . By using appropriate “ diagonalizing ” transformations ( cf . Theorem XII . 3 .

16 ) , we may

**apply**Theorem 21 to analyze a variety of operators . The following...

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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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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