Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 909
Spectral Representation Let и be a finite positive measure defined on the Borel sets B of the complex plane and vanishing on the complement of a bounded set S. One of the simplest examples of a bounded normal operator is the operator T ...
Spectral Representation Let и be a finite positive measure defined on the Borel sets B of the complex plane and vanishing on the complement of a bounded set S. One of the simplest examples of a bounded normal operator is the operator T ...
Page 913
PROOF . We can clearly suppose that \ yol 1. Let Yo , 41 , 42 , • • be an orthonormal basis for H , whose initial element is yo . Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each Borel set e .
PROOF . We can clearly suppose that \ yol 1. Let Yo , 41 , 42 , • • be an orthonormal basis for H , whose initial element is yo . Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each Borel set e .
Page 1900
( See also Boolean ring ) definition , ( 43 ) properties , ( 44 ) representation of , ( 44 ) Boolean ring , definition , ( 40 ) representation of , 1.12.1 ( 41 ) Borel field of sets , definition , III.5.10 ( 137 ) Borel function , X.1 ...
( See also Boolean ring ) definition , ( 43 ) properties , ( 44 ) representation of , ( 44 ) Boolean ring , definition , ( 40 ) representation of , 1.12.1 ( 41 ) Borel field of sets , definition , III.5.10 ( 137 ) Borel function , X.1 ...
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