## Linear Operators: Spectral theory |

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Page 898

If E is the resolution of the identity for the normal operator T and if d is a Borel set

of complex numbers , then E ( 8 ) T = TE ... Let E be the resolution of the identity

for the bounded normal operator T and for each complex

...

If E is the resolution of the identity for the normal operator T and if d is a Borel set

of complex numbers , then E ( 8 ) T = TE ... Let E be the resolution of the identity

for the bounded normal operator T and for each complex

**bounded Borel**function...

Page 910

( c ) for every

every x in H and every ol , ( U ( / ( T ) x ) ) & ( 2 ) = f ( 2 ) ( Ux ) a ( 2 ) , for Mo -

almost all a . We shall first discuss , in the following theorem , the situation where

H ...

( c ) for every

**Borel**function f which is**bounded**on the spectrum of T we have , forevery x in H and every ol , ( U ( / ( T ) x ) ) & ( 2 ) = f ( 2 ) ( Ux ) a ( 2 ) , for Mo -

almost all a . We shall first discuss , in the following theorem , the situation where

H ...

Page 1214

For the kernels W , we take those associated with the elements a in A as in

Lemma 9 so that the statements ( a ) and ( b ) are satisfied . From ( b ) it follows

that 9 , 2012 Ma ( d ) v ( ds ) < oo , n 21 , for each

axis .

For the kernels W , we take those associated with the elements a in A as in

Lemma 9 so that the statements ( a ) and ( b ) are satisfied . From ( b ) it follows

that 9 , 2012 Ma ( d ) v ( ds ) < oo , n 21 , for each

**bounded Borel**set e of the realaxis .

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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