BANACH-SPACES WITH THE 2-SUMMING PROPERTY

A Banach space X has the 2-summing property if the norm of every linear operator from X to a Hilbert space is equal to the 2-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent of the scalar field: the property is self-dual and any space with the property is a finite dimensional space of maximal distance to the Hilbert space of the same dimension. In the case of real scalars only the red line and real l(infinity)(2) have the 2-summing property. In the complex case there are more examples; e.g., all subspaces of complex l(infinity)(3) and their duals.