Hypo-q-norms on cartesian products of algebras of bounded linear operators on Hilbert spaces

Abstract

Abstract: 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.

Keywords

• Hilbert spaces
• bounded linear operators
• operator norm and numerical radius
• n-tuple of operators
• operator inequalities.