Weak metric approximation properties and nice projections | Zendy

Trond A. Abrahamsen | Zendy

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Weak metric approximation properties and nice projections

Author(s) -

Trond A. Abrahamsen

Publication year - 2006

Publication title -

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∗∗).

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