## 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 1947

Let B , , . . . , Bk be a finite collection of commuting bounded Boolean algebras of

projections in a Hilbert space H . Then there exists a bounded self

a self ...

Let B , , . . . , Bk be a finite collection of commuting bounded 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 isa self ...

Page 2170

These lemmas will show that the hypotheses of Theorem 5 . 18 are satisfied by a

self

...

These lemmas will show that the hypotheses of Theorem 5 . 18 are satisfied by a

self

**adjoint operator**in Hilbert space . 1 LEMMA . If T is a bounded self**adjoint****operator**in Hilbert space , its spectrum is real and for every non - real a we have...

Page 2508

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz ... Von Neumann shows that , by adding a Hilbert - Schmidt

class self

) ...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz ... Von Neumann shows that , by adding a Hilbert - Schmidt

class self

**adjoint operator**V to a bounded self**adjoint operator**H such that Ep ( H) ...

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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