Linear Operators: General theory |
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Page 169
5 Show that ( i ) , ( ii ) , and ( iii ) of Theorem 3.6 imply that f is in L , ( S , E , l ) and that in to converges to zero even if { In } is a generalized sequence . 6 Let u be bounded . Suppose that the field E is separable under ...
5 Show that ( i ) , ( ii ) , and ( iii ) of Theorem 3.6 imply that f is in L , ( S , E , l ) and that in to converges to zero even if { In } is a generalized sequence . 6 Let u be bounded . Suppose that the field E is separable under ...
Page 204
Since ulFn ) = Ssa , In ( San ( Usa ) does not converge to zero and since 0 < In ( sa ) si it follows from the dominated convergence theorem ( 6.16 ) that there is a point s . , in Sq , for which In ( $ , ) is defined for all n and for ...
Since ulFn ) = Ssa , In ( San ( Usa ) does not converge to zero and since 0 < In ( sa ) si it follows from the dominated convergence theorem ( 6.16 ) that there is a point s . , in Sq , for which In ( $ , ) is defined for all n and for ...
Page 595
Let , fn be in F ( T ) , and let { f ( T ) / n ( T ) } converge to zero in the weak operator topology . Suppose that { In ( T " ) x } is weakly sequentially compact for each x in X , and that f vanishes at a finite set of points of o ...
Let , fn be in F ( T ) , and let { f ( T ) / n ( T ) } converge to zero in the weak operator topology . Suppose that { In ( T " ) x } is weakly sequentially compact for each x in X , and that f vanishes at a finite set of points of o ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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