Structure of the antieigenvectors of a strictly accretive operator.
Submultiplicative functions and operator inequalities
Let T: C¹(ℝ) → C(ℝ) be an operator satisfying the “chain rule inequality” T(f∘g) ≤ (Tf)∘g⋅Tg, f,g ∈ C¹(ℝ). Imposing a weak continuity and a non-degeneracy condition on T, we determine the form of all maps T satisfying this inequality together with T(-Id)(0) < 0. They have the form Tf = ⎧ , f’ ≥ 0, ⎨ ⎩ , f’ < 0, with p > 0, H ∈ C(ℝ), A ≥ 1. For A = 1, these are just the solutions of the chain rule operator equation. To prove this, we characterize the submultiplicative, measurable functions...
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.
Upper bounds for the Euclidean operator radius and applications.
Vector and operator trapezoidal type inequalities for continuous functions of selfadjoint operators in Hilbert spaces.
Young's (in)equality for compact operators
If a,b are n × n matrices, T. Ando proved that Young’s inequality is valid for their singular values: if p > 1 and 1/p + 1/q = 1, then for all k. Later, this result was extended to the singular values of a pair of compact operators acting on a Hilbert space by J. Erlijman, D. R. Farenick and R. Zeng. In this paper we prove that if a,b are compact operators, then equality holds in Young’s inequality if and only if .
Young's inequality in compact operators. The case of equality.
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