## 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

For an exposition of ordered topological vector spaces , we refer the reader to the

books of Day [ 12 ] , Kelley and ... If X is a real

X1 = X 9 X and define : ( a + iß ) ( x , y ] = [ ax — By , ay + Bx ] , a , ß € R , X , Y ...

For an exposition of ordered topological vector spaces , we refer the reader to the

books of Day [ 12 ] , Kelley and ... If X is a real

**B**-**space**which is ordered by < , letX1 = X 9 X and define : ( a + iß ) ( x , y ] = [ ax — By , ay + Bx ] , a , ß € R , X , Y ...

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 ...

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11 ( Friedrichs ' Identity ) Let H be a Hilbert space , and let B ( H ) be the

of all bounded operators in H . Let y > 0 and 1 > B > 0 be two real numbers , and

let A , . b ( B ( H ) ) be the space of Definition 2 . 13 . For each A € A , 6 ( B ( H ) ) ...

11 ( Friedrichs ' Identity ) Let H be a Hilbert space , and let B ( H ) be the

**B**-**space**of all bounded operators in H . Let y > 0 and 1 > B > 0 be two real numbers , and

let A , . b ( B ( H ) ) be the space of Definition 2 . 13 . For each A € A , 6 ( B ( H ) ) ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 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