Complementably universal Banach spaces, II |
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| Authors: | WB Johnson A Szankowski |
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| Institution: | a Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
b Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel |
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| Abstract: | The two main results are:- A.
- If a Banach space X is complementably universal for all subspaces of c0 which have the bounded approximation property, then X∗ is non-separable (and hence X does not embed into c0).
- B.
- There is no separable Banach space X such that every compact operator (between Banach spaces) factors through X.
Theorem B solves a problem that dates from the 1970s. |
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| Keywords: | Universal Banach spaces Complemented subspaces Approximation property Factorization of compact operators |
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