## Linear Operators: Spectral operators |

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Page 2158

If the set of points

subinterval of To whose end points are

Borel subset of the plane is measurable T . PROOF . Let y be a closed subinterval

of To ...

If the set of points

**regular**relative to T is dense on To , then every closedsubinterval of To whose end points are

**regular**relative to T is in S ( T ) and everyBorel subset of the plane is measurable T . PROOF . Let y be a closed subinterval

of To ...

Page 2159

If the point spectrum of the adjoint T * contains no non - trivial subarc of To , then

the set of points

spectrum of the adjoint of T , then there is no functional xc * # 0 for which x * ( 1 ...

If the point spectrum of the adjoint T * contains no non - trivial subarc of To , then

the set of points

**regular**relative to T is dense in To . PROOF . If , is not in the pointspectrum of the adjoint of T , then there is no functional xc * # 0 for which x * ( 1 ...

Page 2160

It has been shown that an arbitrary vector x in X is the sum of a vector y with ( do I

– T ) y = 0 and a vector x y in the closure of ( No I – T ) X . Since do is interior to an

interval of constancy relative to T , it is therefore a

It has been shown that an arbitrary vector x in X is the sum of a vector y with ( do I

– T ) y = 0 and a vector x y in the closure of ( No I – T ) X . Since do is interior to an

interval of constancy relative to T , it is therefore a

**regular**point relative to T . Q ...### What people are saying - Write a review

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