Hypo-q-Norms on a Cartesian Product of Algebras of Operators on Banach Spaces

Abstract

In this paper we consider the hypo-q-operator norm and hypo-q-numerical radius on a Cartesian product of algebras of bounded linear operators on Banach spaces. A representation of these norms in terms of semi-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.

Keywords

• normed spaces
• cartesian products of normed spaces
• inequalities
• reverse inequalities
• shisha-mond type inequalities
• 46b05
• 26d15