## Linear Operators: Spectral operators |

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Page 2108

are , Let u ( respectively , v ) be a spectral measure on X ( respectively , Y ) to A.

Then in order for there to

contained in a commutative subalgebra of A and that there

of A ...

are , Let u ( respectively , v ) be a spectral measure on X ( respectively , Y ) to A.

Then in order for there to

**exist**a ... and sufficient that the values of u and v arecontained in a commutative subalgebra of A and that there

**exists**a partial orderof A ...

Page 2418

the integral ( 74 ) 1,1416 " , ** { ! | 14:14 | 156 ) de dybder de

" e D. Therefore , by Tonelli's theorem ( III.11.14 ) , the integral D D ( ) ( 75 ) SS ...

**exists**almost everywhere for each fe Î ( D , Y ) , and , using Lemma 5 once more ,the integral ( 74 ) 1,1416 " , ** { ! | 14:14 | 156 ) de dybder de

**exists**for almost all z" e D. Therefore , by Tonelli's theorem ( III.11.14 ) , the integral D D ( ) ( 75 ) SS ...

Page 2441

This shows that there

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

finite constant M " independent of ε such that 22 V4 ( 43 ) 1V4 ( , r ' ) | + av . ( r , r )

+ ...

This shows that there

**exists**a finite absolute constant c ' such that I ( 0 ) < c ' ( 1 +101 ) -n + 1 . Using this inequality and using ( 37 ) , we see that there

**exists**afinite constant M " independent of ε such that 22 V4 ( 43 ) 1V4 ( , r ' ) | + av . ( r , r )

+ ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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