## Linear Operators: Spectral operators |

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Page 2095

Consequently , the analogs of the results stated in the preceding paragraph for

restrictions of spectral and

Although the restrictions of operators with the single valued extension property

have ...

Consequently , the analogs of the results stated in the preceding paragraph for

restrictions of spectral and

**scalar type**operators also hold for their quotients .Although the restrictions of operators with the single valued extension property

have ...

Page 2106

It is proved that if A is adjoint Abelian , then ( i ) ( A2 ) * is a

class ( X ) , and ( ii ) if X is weakly complete , then A ' is a

Moreover , if A is adjoint Abelian and X is weakly complete , then A is

if ...

It is proved that if A is adjoint Abelian , then ( i ) ( A2 ) * is a

**scalar type**operator ofclass ( X ) , and ( ii ) if X is weakly complete , then A ' is a

**scalar type**operator .Moreover , if A is adjoint Abelian and X is weakly complete , then A is

**scalar type**if ...

Page 2174

In a Hilbert space the condition that lett ) S M for all te R implies that T is

equivalent to a self adjoint operator and hence is a

spectrum . ( This follows from Lemma XV . 6 . 1 which implies that the bounded

group G ...

In a Hilbert space the condition that lett ) S M for all te R implies that T is

equivalent to a self adjoint operator and hence is a

**scalar type**operator with realspectrum . ( This follows from Lemma XV . 6 . 1 which implies that the bounded

group G ...

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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