## 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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Results 1-3 of 89

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

X = XX and define : ( a + iß ) [ x , y ] = [ ax — By , ay + Bx ) , a , ße R , X , Y EX ...

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 < , letX = XX and define : ( a + iß ) [ x , y ] = [ ax — By , ay + Bx ) , a , ße R , X , Y EX ...

Page 2482

5 Let In denote the

{ ; - . 12,1 " } 1'p , and let A be the

such that 00 lla || = £ laul < oo . 1.j = 0 Let B be the

...

5 Let In denote the

**B**-**space**of sequences 2 = [ 20 , 21 , ... ] with the norm [ 2 ] = {{ ; - . 12,1 " } 1'p , and let A be the

**B**-**space**of infinite matrices a = { ajj , i , j 2 0 }such that 00 lla || = £ laul < oo . 1.j = 0 Let B be the

**B**-**space**of infinite matrices b...

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E - O + - 8-0 Eie Let H be a Hilbert space , and let B ( H ) be the

bounded operators in H. Let C ( 8 , t ) be a B ( H ) -valued function defined for all

and t , and let fe L2 ( R , H ) . Suppose that || Clly . < 0o , where the norm is as ...

E - O + - 8-0 Eie Let H be a Hilbert space , and let B ( H ) be the

**B**-**space**of allbounded operators in H. Let C ( 8 , t ) be a B ( H ) -valued function defined for all

and t , and let fe L2 ( R , H ) . Suppose that || Clly . < 0o , where the norm is as ...

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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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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