Hadamard product submultiplicativity of certain induced norms

Abstract

In this paper we ask which norms on M_d induced by an absolute vector norm are sub-multiplicative with respect to the Hadamard product. We provide a simple necessary condition for submultiplicativity. We demonstrate that each norm on M_d induced by an l_p norm Hadamard submultiplicative and that the norms induced by certain polyhedral norms are Hadamard submultiplicative. We also consider some related inequalities.

Keywords:

• Hadamard product
• Norm inequalities

^∗Corresponding author, e-mail: [email protected]

^∗Corresponding author, e-mail: [email protected]

Notes

^∗Corresponding author, e-mail: [email protected]