## 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 ...

Page 2484

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 XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero