## Linear Operators: Spectral operators |

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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

sets in X X Y to A such that ( 8 x 0 ) = u ( d ) v ( o ) for all d , o , it is necessary and

...

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

in order for there to

**exist**a necessarily unique spectral measure d on the Bairesets in X X Y to A such that ( 8 x 0 ) = u ( d ) v ( o ) for all d , o , it is necessary and

...

Page 2405

If he L , ( S , E , p ) and 2 Sr < 00 , it follows that the integral SS ( 14 ) ( Ah ) ( s ) = |

A ( s , t ) | h ( t ) q ( dt )

of an element f of L ( S , E , M ) , we have | Ahl , $ { A } , \ h \ , . Thus , using ...

If he L , ( S , E , p ) and 2 Sr < 00 , it follows that the integral SS ( 14 ) ( Ah ) ( s ) = |

A ( s , t ) | h ( t ) q ( dt )

**exists**for u - almost all s , and that , writing | f | , for the normof an element f of L ( S , E , M ) , we have | Ahl , $ { A } , \ h \ , . Thus , using ...

Page 2418

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

almost everywhere for each fe Īp ( D , Y ) , and , using Lemma 5 once more , the

integral ( 74 ) 5 , 14 , 62 " , zv { S , 14 , | 15 ( 2 ) | dx dy Jdx dy

z " e ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

**exists**almost everywhere for each fe Īp ( D , Y ) , and , using Lemma 5 once more , the

integral ( 74 ) 5 , 14 , 62 " , zv { S , 14 , | 15 ( 2 ) | dx dy Jdx dy

**exists**for almost allz " e ...

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