Universal non-compact operators between super-reflexive Banach spaces and the existence of a complemented copy of Hilbert space |
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Authors: | S J Dilworth |
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Institution: | (1) Department of Mathematics, University of Missouri — Columbia, 65211 Columbia, MO, USA |
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Abstract: | Suppose that 1<p≦2, 2≦q<∞. The formal identity operatorI:l
p→l
qfactorizes through any given non-compact operator from ap-smooth Banach space into aq-convex Banach space. It follows that ifX is a 2-convex space andY is an infinite dimensional subspace ofX which is isomorphic to a Hilbert space, thenY contains an isomorphic copy ofl
2 which is complemented inX. |
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Keywords: | |
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