  In this article, we introduce the normal category L(S) [R(S)] of principal
left [right] ideals of the normed algebra S of all finite rank bounded
operators on a Hilbert space H and is shown that they are isomorphic, using
Hilbert space duality. We also described the semigroup of all normal cones in
L(S) which is isomorphic to the semigroup of all finite rank operators on H.
Further, we construct bounded normal cones in L(S) such that the set of all
bounded normal cones in L(S) is a normed algebra isomorphic to the normed
algebra S.
