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

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Page 2162

Thus , in view of

that T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if

the points regular relative to T are dense on to . Thus Lemmas 12 , 13 , 14 give ...

Thus , in view of

**Theorem**4 . 5 , to prove the present**theorem**it suffices to showthat T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if

the points regular relative to T are dense on to . Thus Lemmas 12 , 13 , 14 give ...

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21

be a function analytic in a domain U which , when taken together with a finite

number of exceptional points p , includes a neighborhood of o ( T ) and a ...

21

**THEOREM**. Let T be a spectral operator , and E its resolution of identity . Let fbe a function analytic in a domain U which , when taken together with a finite

number of exceptional points p , includes a neighborhood of o ( T ) and a ...

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32

space X and let B * be the Boolean algebra of adjoints in B * . Then a projection E

in B has finite uniform multiplicity n if and only if its adjoint E * in B * has finite ...

32

**THEOREM**. Let B be a complete Boolean algebra of projections in a Banachspace X and let B * be the Boolean algebra of adjoints in B * . Then a projection E

in B has finite uniform multiplicity n if and only if its adjoint E * in B * has finite ...

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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 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