## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2084

Using the fact that the difference R ( A ; A ) – R ( A ; B ) is analytic for 1 + , prove

that C is a quasi - nilpotent operator and that R ( 1 ; A ) = R ( 1 ; B ) + R ( 1 ; C ) – –

55 ( McCarthy ) Let T be a spectral operator in a

Using the fact that the difference R ( A ; A ) – R ( A ; B ) is analytic for 1 + , prove

that C is a quasi - nilpotent operator and that R ( 1 ; A ) = R ( 1 ; B ) + R ( 1 ; C ) – –

55 ( McCarthy ) Let T be a spectral operator in a

**complex**B - space X which ...Page 2171

The symbol T is a bounded linear operator on a

in X the symbol [ x ] will be used for the closed linear manifold determined by all

the vectors R ( E ; T ' ) x with & in p ( T ) . If o is a closed set of

The symbol T is a bounded linear operator on a

**complex**B - space X . For each xin X the symbol [ x ] will be used for the closed linear manifold determined by all

the vectors R ( E ; T ' ) x with & in p ( T ) . If o is a closed set of

**complex**numbers ...Page 2188

Let E be a spectral measure in the

countably additive on a o - field of subsets of a set 1 and let g be a bounded Borel

measurable function defined on the

...

Let E be a spectral measure in the

**complex**B - space X which is defined andcountably additive on a o - field of subsets of a set 1 and let g be a bounded Borel

measurable function defined on the

**complex**plane . Then 2 ) ) E ( d ) ) = l g ( u ) E...

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