## 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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Results 1-3 of 75

Page 2305

8 , 0 ( L ) is the set of numbers in = ( n + a + B + 1 ) ( n + a + B ) , and each

eigenspace

immediately from Corollary 9 that L + B is a spectral operator for each bounded

operator ...

8 , 0 ( L ) is the set of numbers in = ( n + a + B + 1 ) ( n + a + B ) , and each

eigenspace

**corresponding**to these eigenvalues is one - dimensional . It followsimmediately from Corollary 9 that L + B is a spectral operator for each bounded

operator ...

Page 2341

This follows from ( 58 ) by an argument using Lemma 7 , which is similar to the

same way that the collection of all finite sums of projections Elàm ; T ) is uniformly

...

This follows from ( 58 ) by an argument using Lemma 7 , which is similar to the

**corresponding**argument used in the discussion of Case 1A . It follows in thesame way that the collection of all finite sums of projections Elàm ; T ) is uniformly

...

Page 2507

Faddeev shows that if H is the six - dimensional Laplacian , and V is a sum of

three multiplication operators ( each

body system ) , then the spectrum of H + V consists of the purely continuous ...

Faddeev shows that if H is the six - dimensional Laplacian , and V is a sum of

three multiplication operators ( each

**corresponding**to a twobody force in a three -body system ) , then the spectrum of H + V consists of the purely continuous ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact 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