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

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Page 2025

Since Eks ( 8 ) # 0 there is a vector y ( s ) in EP with 14 ( s ) = 1 and ( s ) = Êky ( 8 )

( s ) . Thus , since Ékj ( s ) and Exq ( s ) are disjoint projections if q # j , it follows

from ( 35 ) that R ( A ; Â ( s ) ) " } ( s ) = 4 ( s ) ( a – dxy ( s ) ) - - and ( 39 )

...

Since Eks ( 8 ) # 0 there is a vector y ( s ) in EP with 14 ( s ) = 1 and ( s ) = Êky ( 8 )

( s ) . Thus , since Ékj ( s ) and Exq ( s ) are disjoint projections if q # j , it follows

from ( 35 ) that R ( A ; Â ( s ) ) " } ( s ) = 4 ( s ) ( a – dxy ( s ) ) - - and ( 39 )

**gives**ver...

Page 2031

To prove ( iv ) suppose first that y is in 0 in which case a permissible interchange

of integration

, OEO . " RN RN ' Now 0 is dense in H = L2 ( RN ) and thus there is for an ...

To prove ( iv ) suppose first that y is in 0 in which case a permissible interchange

of integration

**gives**( FT ) ) ( Q ) = 1 ( FP ) ( s ) ¥ ( s ) ds p ( s ) ( F4 ) ( s ) ds = Tfvlo ), OEO . " RN RN ' Now 0 is dense in H = L2 ( RN ) and thus there is for an ...

Page 2065

Thus the Gelfand theory

not an element possesses an inverse and so ... In order to apply this procedure to

a given algebra , it is sufficient to

...

Thus the Gelfand theory

**gives**a general procedure for determining whether ornot an element possesses an inverse and so ... In order to apply this procedure to

a given algebra , it is sufficient to

**give**a satisfactory representation of its spectrum...

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