## Linear Operators: Spectral operators |

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Page 2092

The relation of being quasi - nilpotent

relation and , when T and U are quasi - nilpotent

U ) , ( ii ) T has the single valued extension property if and only if U does , and ( iii

) if T ...

The relation of being quasi - nilpotent

**equivalent**is indeed an equivalencerelation and , when T and U are quasi - nilpotent

**equivalent**, then ( i ) o ( T ) = 0 (U ) , ( ii ) T has the single valued extension property if and only if U does , and ( iii

) if T ...

Page 2105

Berkson [ 2 ] showed that if E is a bounded spectral measure and if one defines | |

a | | = sup { var x * E ( - ) 12 * 1 = 1 } , then | | · | | is a norm

relative to which all the operators E ( 8 ) become Hermitian . It follows from this ...

Berkson [ 2 ] showed that if E is a bounded spectral measure and if one defines | |

a | | = sup { var x * E ( - ) 12 * 1 = 1 } , then | | · | | is a norm

**equivalent**to 1 : 1 andrelative to which all the operators E ( 8 ) become Hermitian . It follows from this ...

Page 2115

It is proved that if T is decomposable and T and U are quasi - nilpotent

, then U is decomposable . Moreover , if T and U are decomposable , then X7 ( F )

= Xu ( F ) for all closed sets F if and only if T and U are quasi - nilpotent ...

It is proved that if T is decomposable and T and U are quasi - nilpotent

**equivalent**, then U is decomposable . Moreover , if T and U are decomposable , then X7 ( F )

= Xu ( F ) for all closed sets F if and only if T and U are quasi - nilpotent ...

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