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| Harun Al-Rashid... |
 Posted: Fri Nov 06, 2009 1:40 pm |
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Let (T_n) in L(E,F), where
E is the sequence Banach space l_infinity, and
F is the sequence Banach space l_1,
s.t. ||T_n|| <= 1 for all n.
Is it true that (T_n) has a pointwisely convergent subsequence (T_n_k), i.e. there is some T in L(E,F) s.t.
T_n_k(x) -> Tx for all x in E ? If so, why ?
TIA |
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| Harun Al-Rashid... |
| Posted: Fri Nov 06, 2009 1:56 pm |
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Guest
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[quote]Let (T_n) in L(E,F), where
E is the sequence Banach space l_infinity, and
F is the sequence Banach space l_1,
s.t. ||T_n|| <= 1 for all n.
Is it true that (T_n) has a pointwisely convergent
subsequence (T_n_k), i.e. there is some T in L(E,F)
s.t.
T_n_k(x) -> Tx for all x in E ? If so, why ?
TIA
[/quote]
I mean T_n_k(x) -> Tx in the weak-star topology of l_1. |
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