Linear Operators: Spectral theory |
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Page 1036
Then the infinite product 8 ( T ) = } ( 1 - 1 ) er converges and defines a function
analytic for a + 0 . For each fixed a + 0 , 8 ( T ) is a continuous complex valued
function on the B - space of all Hilbert - Schmidt operators . PROOF . First note
that if ...
Then the infinite product 8 ( T ) = } ( 1 - 1 ) er converges and defines a function
analytic for a + 0 . For each fixed a + 0 , 8 ( T ) is a continuous complex valued
function on the B - space of all Hilbert - Schmidt operators . PROOF . First note
that if ...
Page 1333
Since gn + 0 and TR ( 2 ; T ) is a bounded operator , it follows that R ( 2 ; T ) gn
and TR ( 1 ; T ) gn converge to zero in L ( I ) . Thus by Lemma 2 . 16 the series on
( 4 , 9 : 19 ; converges to f in the topology of Cn - ( J ) for each compact interval J
of ...
Since gn + 0 and TR ( 2 ; T ) is a bounded operator , it follows that R ( 2 ; T ) gn
and TR ( 1 ; T ) gn converge to zero in L ( I ) . Thus by Lemma 2 . 16 the series on
( 4 , 9 : 19 ; converges to f in the topology of Cn - ( J ) for each compact interval J
of ...
Page 1436
Let { gn } be a bounded sequence of elements of D ( T ) such that { Tgn }
converges . Find a subsequence { & n , } = { hi } such that x * ( hi ) converges for
each j , 1 si sk . Then hi = h ; - * - * * ( hi ) ; is in D , and Tħ ; = Thị . Thus { ħi }
converges ...
Let { gn } be a bounded sequence of elements of D ( T ) such that { Tgn }
converges . Find a subsequence { & n , } = { hi } such that x * ( hi ) converges for
each j , 1 si sk . Then hi = h ; - * - * * ( hi ) ; is in D , and Tħ ; = Thị . Thus { ħi }
converges ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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