## Linear Operators: Spectral operators |

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Page 1939

If S and N are bounded commuting operators and if N is quasi - nilpotent , then o ( 8 + N ) = o ( S ) . ... A bounded operator T is a

If S and N are bounded commuting operators and if N is quasi - nilpotent , then o ( 8 + N ) = o ( S ) . ... A bounded operator T is a

**spectral operator**if and only if it is the sum T = S + N of a bounded scalar type operator S and a ...Page 2118

A generalized scalar

A generalized scalar

**operator**Te B ( X ) is said to be regular if it has a regular**spectral**distribution . Although it is not known whether or not every generalized scalar**operator**is regular ( unless the**spectrum**is sufficiently “ thin ...Page 2590

Restriction of a

Restriction of a

**spectral operator**, spectrum of , XV.8.5 ( 1956 ) Quantum mechanical three - body problem , XX.6 ( 2501 ) , ( 2507 ) Quantum theory of fields , XX.6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator , definition of ...### 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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### Common terms and phrases

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