The arithmetic-geometric mean and its generalizations for noncommuting linear operators
The calculus of operator functions and operator convexity [Book]
The Fuglede-Putnam theorem and Putnam's inequality for quasi-class (A, k) operators.
The minimal operator and the John--Nirenberg theorem for weighted grand Lebesgue spaces
We introduce the minimal operator on weighted grand Lebesgue spaces, discuss some weighted norm inequalities and characterize the conditions under which the inequalities hold. We also prove that the John-Nirenberg inequalities in the framework of weighted grand Lebesgue spaces are valid provided that the weight function belongs to the Muckenhoupt class.
The upper bound of a reserve Hölder's type operator inequality and its applications.