## Linear Operators: Spectral operators |

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Page 1928

... how far the theory may be applied to non - symmetric boundary value problems

. 2 . Terminology and Preliminary Notions The concepts of a Boolean algebra of

... how far the theory may be applied to non - symmetric boundary value problems

. 2 . Terminology and Preliminary Notions The concepts of a Boolean algebra of

**projections**, a spectral measure , an integral with respect to a spectral measure ...Page 2218

Proof . Since a spectral operator of scalar type is clearly in the weakly closed

algebra A generated by the

to show that every operator in A is a spectral operator of scalar type . This follows

...

Proof . Since a spectral operator of scalar type is clearly in the weakly closed

algebra A generated by the

**projections**in its resolution of the identity , it sufficesto show that every operator in A is a spectral operator of scalar type . This follows

...

Page 2300

Then , since the collection of finite sums of

bounded , it is clear from [ * ] that the collection of finite sums of

T + P ) , n 2 K , is uniformly bounded . Moreover , Lan ( E ( An ; T ) – Elun ; T + P )

...

Then , since the collection of finite sums of

**projections**E ( Nn ; T ) is uniformlybounded , it is clear from [ * ] that the collection of finite sums of

**projections**ElMn ;T + P ) , n 2 K , is uniformly bounded . Moreover , Lan ( E ( An ; T ) – Elun ; T + P )

...

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