Advancement of Numerical Radius Inequalities of Operators and Product of Operators

On Cauchy–Schwarz type inequalities and applications to numerical radius inequalities

“…In recent times, several researchers have improved the Cauchy-Schwarz inequality through various approaches. We encourage readers to explore the referenced articles [3,7,10,17,21] for further insight. Let B(H) denote the C * -algebra of all bounded linear operators on a complex Hilbert space H. The absolute value of T, is defined as |T | = (T * T ) 1 2 , where T * represents the Hilbert adjoint of the operator T. The numerical range of T ∈ B(H) is denoted by W (T ), is the image of the unit sphere of H under the mapping x T x, x .…”