Open AccessWeak metric approximation properties and nice projections
Author(s) -
Trond A. Abrahamsen
Publication year - 2006
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2006.10.03
Subject(s) - projection (relational algebra) , banach space , mathematics , metric (unit) , space (punctuation) , norm (philosophy) , combinatorics , metric space , closure (psychology) , discrete mathematics , computer science , algorithm , operations management , political science , law , economics , operating system , market economy
We prove that a Banach space X has the weak MAP (the weak MCAP) [the very weak MCAP] if and only if there exists a norm one projection P on X∗∗ with X⊂P(X∗∗) such that P is in the weak∗-closure of F(X,X) (K(X,X)) [K(X,X∗∗)] in L(X∗∗,X∗∗).