## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 1947

Let B1 , . . . , 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 B1 , . . . , 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 2478

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

Theodore Schwartz. 19 LEMMA . Let H4 be a self

domain D ( H , ) and resolution of the identity E4 ( : ) . Suppose that V4 is a

symmetric ...

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

Theodore Schwartz. 19 LEMMA . Let H4 be a self

**adjoint operator**in H , withdomain D ( H , ) and resolution of the identity E4 ( : ) . Suppose that V4 is a

symmetric ...

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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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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