Computability-theoretic complexity of effective Banach spaces
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<p><b>We investigate the geometry of effective Banach spaces, namely a sequenceof approximation properties that lies in between a Banach space having a basis and the approximation property.</b></p> <p>We establish some upper bounds on suchproperties, as well as proving some arithmetical lower bounds. Unfortunately,the upper bounds obtained in some cases are far away from the lower bound.</p> <p>However, we will show that much tighter bounds will require genuinely newconstructions, and resolve long-standing open problems in Banach space theory.</p> <p>We also investigate the effectivisations of certain classical theorems in Banachspaces.</p>
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2009 ◽
Vol 139
(3)
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pp. 551-565
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2005 ◽
Vol 71
(1)
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pp. 107-111
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1992 ◽
Vol 34
(2)
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pp. 229-239
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1991 ◽
Vol 44
(1)
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pp. 75-90
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1993 ◽
Vol 03
(04)
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pp. 313-320
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