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

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Page 2160

It will next be

) X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that x * ( x - y

) = 0 for every linear functional a * which vanishes on ( 101 – T ) X . If x * is ...

It will next be

**shown**that the vector x - y is in the closure of the manifold ( 101 – T ') X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that x * ( x - y

) = 0 for every linear functional a * which vanishes on ( 101 – T ) X . If x * is ...

Page 2226

... bounded Boolean algebra of projections on X , then X has an equivalent norm

such that the functionals given by Lemma 3 . 12 can be expressed by means of a

semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ) has

... bounded Boolean algebra of projections on X , then X has an equivalent norm

such that the functionals given by Lemma 3 . 12 can be expressed by means of a

semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ) has

**shown**that in ...Page 2360

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

Theodore Schwartz. It will be

and i sufficiently large . From this it will then follow as above that the function f ( u

) ...

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

Theodore Schwartz. It will be

**shown**below that | T ' ' R ( u ; T ) A S | for u in V ,and i sufficiently large . From this it will then follow as above that the function f ( u

) ...

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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