Hypo-q-Norms on Cartesian Products of Algebras of Bounded Linear Operators on Hilbert Spaces

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δp, ϑp and the real norms ηr,p and θr,p are provided as well.