## Linear Operators: Spectral operators |

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Page 2118

A generalized scalar

scalar

two ...

A generalized scalar

**operator**T e B ( X ) is said to be regular if it has a regular**spectral**distribution . Although it is not known whether or not every generalizedscalar

**operator**is regular ( unless the**spectrum**is sufficiently " thin " ) , given anytwo ...

Page 2249

Then , by Theorem 9 ( ii ) and Lemma 19 , T | E ( e ) X is a bounded

o ( T | E ( e ) X ) 2 Z . By the

Theorem VII . 3 . 11 ) and by Theorem 9 ( ii ) , Theorem 9 ( i ) , and Corollary 20 , it

...

Then , by Theorem 9 ( ii ) and Lemma 19 , T | E ( e ) X is a bounded

**operator**ando ( T | E ( e ) X ) 2 Z . By the

**spectral**mapping theorem for bounded**operators**(Theorem VII . 3 . 11 ) and by Theorem 9 ( ii ) , Theorem 9 ( i ) , and Corollary 20 , it

...

Page 2590

Restriction of a

mechanical three - body problem , XX . 6 ( 2501 ) , ( 2507 ) Quantum theory of

fields , XX . 6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator , definition of , XV . 4 . 2

( 1938 ) ...

Restriction of a

**spectral operator**, spectrum of , XV . 8 . 5 ( 1956 ) Quantummechanical three - body problem , XX . 6 ( 2501 ) , ( 2507 ) Quantum theory of

fields , XX . 6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator , definition of , XV . 4 . 2

( 1938 ) ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

29 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 defined Definition denote dense determined differential operator discrete domain elements equation equivalent established exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear 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