Normal type structures and superreflexivity.
Normal type structures and superreflexivity.
It has recently been proved that in any Banach space uniformly normal structure (UNS) implies reflexivity. Here it is proved that in Banach spaces with l.u.st. (local unconditional structure), UNS implies also superreflexivity. An example shows that the analogous result does not hold for a property of normal type, weaker than UNS, which still is known to imply reflexivity.
Geometry and structure of normed linear spaces, Duality and reflexivity in normed linear and Banach spaces, local unconditional structure, uniformly normal structure, reflexivity, superreflexivity
Geometry and structure of normed linear spaces, Duality and reflexivity in normed linear and Banach spaces, local unconditional structure, uniformly normal structure, reflexivity, superreflexivity
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