Density of adjoint operators - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T08:20:58Z http://mathoverflow.net/feeds/question/111079 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111079/density-of-adjoint-operators Density of adjoint operators Slavoj Žižek 2012-11-01T00:07:21Z 2012-11-01T00:07:21Z <p>I am interested in operators on a non-reflexive Banach space. Let \$X\$ be a Banach space and let \$L(X)\$ be the algebra of operators acting on \$X\$. We may embed \$L(X)\$ into \$L(X^{\ast\ast})\$ by \$\Phi(T)=T^{\ast\ast}\$; this is an algebra homomorphism. Is the image \$\Phi(L(X))\$ dense in \$L(X^{**})\$ in the sense of some of the classical operator topologies like WOT, SOT etc.?</p>