Geometry of operator spaces (Q1345487)

The authors investigate the position of \(K(X, Y)\), the space of compact linear operators between Banach spaces \(X\) and \(Y\), in \(L(X, Y)\), the space of bounded linear operators. The position is characterized in terms of M-ideals and unique Hahn-Banach extensions of continuous linear functionals from \(K(X, Y)\) to \(L(X, Y)\). In particular, the authors investigated the class of spaces \(Y\) for which \(K(\ell_ 1, Y)\) is an M- ideal in \(L(\ell_ 1, Y)\) and an important role of the case \(X= \ell_ 1\) in the present context.