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

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Page 2189

Thus the map f→ S ( f ) is a continuous homomorphism of EB ( 1 , 2 ) onto an

algebra of operators S ( f ) . To see that S ( f ) is a scalar type operator with the

stated resolution of the identity ,

the ...

Thus the map f→ S ( f ) is a continuous homomorphism of EB ( 1 , 2 ) onto an

algebra of operators S ( f ) . To see that S ( f ) is a scalar type operator with the

stated resolution of the identity ,

**let f**be in EB ( 1 , 2 ) and , for every Borel set 8 inthe ...

Page 2248

Let T be a spectral operator , and E its resolution of identity .

analytic in a domain U which , when taken together with a finite number of

exceptional points p , includes a neighborhood of o ( T ) and a neighborhood of

the point ...

Let T be a spectral operator , and E its resolution of identity .

**Let f**be a functionanalytic in a domain U which , when taken together with a finite number of

exceptional points p , includes a neighborhood of o ( T ) and a neighborhood of

the point ...

Page 2488

( Hint : Consider A self adjoint , and expand in the eigenvectors of A . ) 17 ( a )

) denote its total variation . Show that perf ( x ) dx = 2 max [ f ( x ) ] + V ( ) .

( Hint : Consider A self adjoint , and expand in the eigenvectors of A . ) 17 ( a )

**Let****f**be a continuous function of bounded variation on an interval [ a , b ] , and let V ( f) denote its total variation . Show that perf ( x ) dx = 2 max [ f ( x ) ] + V ( ) .

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