## 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

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 ...Page 2106

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

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

**scalar type**operator of class ( X ) , and ( ii ) if X is weakly complete , then A2 is a**scalar type**operator . Moreover , if A is adjoint Abelian and X is weakly ...Page 2174

In a Hilbert space the condition that lett | M for all te R implies that T is equivalent to a self adjoint operator and hence is a

In a Hilbert space the condition that lett | M for all te R implies that T is equivalent to a self adjoint operator and hence is a

**scalar type**operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero