TY - JOUR
T1 - Complementably universal Banach spaces, II
AU - Johnson, W. B.
AU - Szankowski, A.
PY - 2009/12/1
Y1 - 2009/12/1
N2 - 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.
AB - 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.
KW - Approximation property
KW - Complemented subspaces
KW - Factorization of compact operators
KW - Universal Banach spaces
UR - http://www.scopus.com/inward/record.url?scp=70349786517&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2009.07.008
DO - 10.1016/j.jfa.2009.07.008
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AN - SCOPUS:70349786517
SN - 0022-1236
VL - 257
SP - 3395
EP - 3408
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 11
ER -