Linear Operators, Part 2 |
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Page 861
If To exists in B ( x ) , then Tx [ ( T2 + y ) 2 ] = yz , ( To ' y ) 2 = T ( yz ) , and if a =
Tote , then az = Totz for every ze X . Also xa = Tya = e = T ; ' ( Tee ) = T ; " ex ) = ( T
' e ) x = ax . Thus x - 1 exists and T ; % = x - 1 % . 2 DEFINITION . An element « in
...
If To exists in B ( x ) , then Tx [ ( T2 + y ) 2 ] = yz , ( To ' y ) 2 = T ( yz ) , and if a =
Tote , then az = Totz for every ze X . Also xa = Tya = e = T ; ' ( Tee ) = T ; " ex ) = ( T
' e ) x = ax . Thus x - 1 exists and T ; % = x - 1 % . 2 DEFINITION . An element « in
...
Page 1057
Thus , to complete the proof of the present lemma , it suffices to show that [ 2 ( y )
12 ( y ) ( 3 ) O ( u ) = P eiyu dy = lim eiyu dy E - > JeslySR y " Jen lyn R - 00 exists
for each u . By Lemma 2 , the integral 0 ( tu ) exists if 0 ( u ) exists and t > 0 ; and ...
Thus , to complete the proof of the present lemma , it suffices to show that [ 2 ( y )
12 ( y ) ( 3 ) O ( u ) = P eiyu dy = lim eiyu dy E - > JeslySR y " Jen lyn R - 00 exists
for each u . By Lemma 2 , the integral 0 ( tu ) exists if 0 ( u ) exists and t > 0 ; and ...
Page 1261
23 If an operator T has a closed linear extension there exists a unique closed
linear extension T such that if T , is any closed linear extension of T then ICT . T is
called the closure of T . ( a ) There exists a densely defined operator with no
closed ...
23 If an operator T has a closed linear extension there exists a unique closed
linear extension T such that if T , is any closed linear extension of T then ICT . T is
called the closure of T . ( a ) There exists a densely defined operator with no
closed ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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