THE NONCOMMUTATIVE l1-l2 INEQUALITY FOR HILBERT C*-MODULES AND THE EXACT CONSTANT

Abstract

Let A be a unital C*-algebra. Then it follows that (Formula Presented) By modifications of arguments of Botelho-Andrade, Casazza, Cheng, and Tran given in 2019, for certain n-tuple x = (Formula Presented), we give a method to compute a positive element cx in the C*-algebra A such that the equality (Formula Presented) holds. We give an application for the integral of Kasparov. We also derive a formula for the exact constant for the continuous l<inf>1</inf> - l<inf>2</inf> inequality. © 2022. Kyungnam University Press