## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2130

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. K = { x € V10 S x } is called the ... we employ the following

construction . If X is a real

define ...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. K = { x € V10 S x } is called the ... we employ the following

construction . If X is a real

**B**-**space**which is ordered by < , let X , = X X anddefine ...

Page 2193

Q . E . D . The preceding corollary is not true if the Hilbert space is replaced by an

arbitrary

commuting scalar type spectral operators in a space of continuous functions ...

Q . E . D . The preceding corollary is not true if the Hilbert space is replaced by an

arbitrary

**B**-**space**, for it has been shown by Kakutani [ 15 ] that the sum of twocommuting scalar type spectral operators in a space of continuous functions ...

Page 2482

5 Let le denote the

{ - 12 , } 1 / P , and let A be the

that Wall = È lagl < co . Let B be the

5 Let le denote the

**B**-**space**of sequences 2 = [ 20 , 21 , . . . ) with the norm [ 2 ] ={ - 12 , } 1 / P , and let A be the

**B**-**space**of infinite matrices a = { aj , i , j 20 } suchthat Wall = È lagl < co . Let B be the

**B**-**space**of infinite matrices b = { bus , i , j 2 ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 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 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