## Linear Operators: Spectral operators |

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Page 2108

143 ] used the word “ spectral ” ) if there

measure u on X to A and a bounded Baire measurable function f : X → C such

that a = sf ( x ) u ( dx ) . It follows that there

on a ...

143 ] used the word “ spectral ” ) if there

**exists**a compact space X , a spectralmeasure u on X to A and a bounded Baire measurable function f : X → C such

that a = sf ( x ) u ( dx ) . It follows that there

**exists**a spectral measure va definedon a ...

Page 2418

, the integral ( 74 ) $ _ 14462 " , 2 ) { S , 1 4363 , | 15 ( 2 ) de ' dy de dy

almost all z " e D . Therefore , by Tonelli ' s theorem ( III . 11 . 14 ) , the integral ...

**exists**almost everywhere for each fe ip ( D , Y ) , and , using Lemma 5 once more, the integral ( 74 ) $ _ 14462 " , 2 ) { S , 1 4363 , | 15 ( 2 ) de ' dy de dy

**exists**foralmost all z " e D . Therefore , by Tonelli ' s theorem ( III . 11 . 14 ) , the integral ...

Page 2441

This shows that there

lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there

constant M " independent of ε such that Lav ( 43 ) 1V4 ( , r ' ) ] + ( r , g ' ) Lav + a ...

This shows that there

**exists**a finite absolute constant c ' such that I ( 0 ) Śc ' ( 1 +lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there

**exists**a finiteconstant M " independent of ε such that Lav ( 43 ) 1V4 ( , r ' ) ] + ( r , g ' ) Lav + a ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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