Banach lattice with AP but without BAP?

Is there an example of a Banach lattice with the approximation property of Grothendieck, but without the MAP (metric approximation property)?

edited Oct 10 2010 at 6:14

Yemon Choi
8,446●1●19●44

asked Jul 12 2010 at 11:36

Oleg Reinov
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What does MAP refer to? – Jesse Madnick Jul 12 2010 at 13:36

Vote to close. 3rd junk post by this member. – supercooldave Jul 12 2010 at 13:45

MAP = metric approximation property. – Yemon Choi Jul 12 2010 at 18:01

Definitely NOT a junk post. Unlike Reinov's other question, this one is not a well known problem and the answer might be simple given known techniques. While Reinov should become aware of proper MO protocol, he deserves respect. I do not know him personally, but along with many other experts I value highly his research on approximation properties. – Bill Johnson Jul 12 2010 at 18:49

Casting 2nd vote to reopen. While I don't know enough about Banach spaces to judge the question, I am happy to take Bill Johnson's word for it. Can I also suggest that deleting the banach-spaces tag seems to have been unwise, because it reduced the chances of the question being seen by (specialist) people who could judge it. – Yemon Choi Jul 12 2010 at 20:14

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