Two-dimensional reductions of the cone of positive diagonal operators in ℓ2

Abstract

The article discusses two-dimensional reductions of the cone of positive diagonal operators in l2. The set of all bounded linear operators acting on the Hilbert space is also considered. It is shown that there is no two-dimensional orthoprojector in the Hilbert space l2 for which the reduction of the cone of positive diagonal operators coincides with the reduction of the cone of all bounded positive operators.