Kikianty and Dragomir (Math Inequal Appl 13:1–32, 2010)
introduced the p−HH norms on the Cartesian square of a normed space,
which are equivalent, but are geometrically different, to the well-known
p-norms. In this paper, notions of orthogonality in terms of the 2 − HH
norm are introduced; and their properties are studied. Some characterizations
of inner product spaces are established, as well as a characterization
of strictly convex spaces.