A note on a conjecture about Wielandt’s inequality

Complementary inequalities to improved AM-GM inequality

“…At the end, in Theorem D we obtain accurate upper bound for operator Wielandt inequality, which is closely related to operator Kantorovich inequality. Our result is more extensive and precise than many previous results due to Fu and He [4] and Gumus [7].…”

Improved Kantorovich and Wielandt operator inequalities for positive linear maps

“…Recently, Fu and He [6] attempt to solve the conjecture and get a step closer to the conjecture. But Gumus [8] obtain a better upper bound to approximate the right side of (3.1) based on…”

Some results around quadratic maps

“…The study of linear maps on an algebra of bounded linear operators on a Hilbert space has been developed by many authors (see for instance [3,5,7,13,14]). Also, for a host of positive linear map inequalities, and for diverse applications of these inequalities, we refer to [8,11,15], and references therein. As is known to all, the linear property plays an important role to obtain this inequalities.…”