Square and cube? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T00:07:14Z http://mathoverflow.net/feeds/question/83262 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83262/square-and-cube Square and cube? Sellapan Nathan 2011-12-12T17:30:44Z 2011-12-12T17:30:44Z <p>Gowers and Maurey proved in their remarkable paper(s), that there is a Banach space \$X\$ such that \$X\$ is isomorphic to its cube \$X\oplus X\oplus X\$ but not to isomorphic to its square \$X\oplus X\$. This space seems to be not a dual space, am I correct? Is there a solution to this problem which is a dual space?</p> <p>And the second quick question: what is the status of the following conjecture:</p> <p><em>There is a Banach space \$X\$ such that \$X\$ is not isomorphic to \$X^2\$ but \$X^2\$ is isomorphic to \$X^3\$?</em></p> <p>Thank you very much. S.</p>