On Jensen’s inequality for the power function of norm of bounded linear operators

Abstract

Abstract Some Jensen’s inequalities for the power function of norm of bounded linear operators are proposed. First, a Jensen’s inequality for a power function on ℝ is investigated. Based on it, Jensen’s inequality for the power function of norm of bounded linear operators is established. Finally, the discussion extends to the polynomial with non-negative coefficients of the power function of the norm, and corresponding Jensen’s inequality is obtained.