## 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 2108

Let u ( respectively , v ) be a spectral measure on X ( respectively , Y ) to A. Then in order for there to

Let u ( respectively , v ) be a spectral measure on X ( respectively , Y ) to A. Then in order for there to

**exist**a ... in a commutative subalgebra of A and that there**exists**a partial order of A for which both M and v are positive .Page 2405

S If he L , ( S , E , u ) and 2 < r < 0 , it follows that the integral ( 14 ) ( Ah ) ( s ) = S14 ( 8,0 ) | h ( t ) u ( dt )

S If he L , ( S , E , u ) and 2 < r < 0 , it follows that the integral ( 14 ) ( Ah ) ( s ) = S14 ( 8,0 ) | h ( t ) u ( dt )

**exists**for u - almost all s , and that , writing Isl , for the norm of an element f of L , ( S , E , ) , we have ...Page 2418

**exists**almost everywhere for each fe Îy ( D , Y ) , and , using Lemma 5 once more , the integral A2 ( , z ' ) ( 74 ) 5,144 " ** | 14:14 | 1563 ) dy'de , » { S . 2 " If ( z ' ) | dx ' dy ' dx dy D 2 –**exists**for almost all z " e D.### What people are saying - Write a review

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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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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