## Linear Operators: Spectral operators |

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Page 2147

Conversely , let the bounded

C ) . Then , by Theorem 3 . 11 and Lemma 3 , T is a spectral operator of class ( S (

T ) , X * ) with a resolution of the identity which is countably additive in the ...

Conversely , let the bounded

**linear operator**T satisfy conditions ( A ) , ( B ) , and (C ) . Then , by Theorem 3 . 11 and Lemma 3 , T is a spectral operator of class ( S (

T ) , X * ) with a resolution of the identity which is countably additive in the ...

Page 2162

If the bounded

and ( G ) then , by Lemma 4 , it has properties ( A ) and ( C ) . Thus , in view of

Theorem 4 . 5 , to prove the present theorem it suffices to show that T has

property ...

If the bounded

**linear operator**T in a weakly complete space has properties ( B )and ( G ) then , by Lemma 4 , it has properties ( A ) and ( C ) . Thus , in view of

Theorem 4 . 5 , to prove the present theorem it suffices to show that T has

property ...

Page 2400

The basic idea of Friedrichs ' method may be expressed heuristically as follows .

Let X be a B - space , and let T be a

...

The basic idea of Friedrichs ' method may be expressed heuristically as follows .

Let X be a B - space , and let T be a

**linear operator**in X ; let K be a second**linear****operator**in X which is , in a sense to be made precise below , very small relative...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined 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 perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero