A characterization of chaotic order.
A characterization of chaotic order and a problem.
A characterization of operator order via grand Furuta inequality.
A note on -hyponormal operators.
A short proof of the best possibility for the grand Furuta inequality.
Additive combinations of special operators
This is a survey paper on additive combinations of certain special-type operators on a Hilbert space. We consider (finite) linear combinations, sums, convex combinations and/or averages of operators from the classes of diagonal operators, unitary operators, isometries, projections, symmetries, idempotents, square-zero operators, nilpotent operators, quasinilpotent operators, involutions, commutators, self-commutators, norm-attaining operators, numerical-radius-attaining operators, irreducible operators...
Aluthge transforms of -hyponormal operators.
Analytic formulas for the hyperbolic distance between two contractions
In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values...
Another consequence of tanahashi’s argument on best possibility of the grand Furuta inequality
We show that Tanahashi’s argument on best possibility of the grand Furuta inequality has an additional consequence.
Antieigenvalue analysis for continuum mechanics, economics, and number theory
My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly...
Antieigenvalue inequalities in operator theory.
Antieigenvectors of the generalized problem and an operator inequality complementary to Schwarz's inequality.
Around the Furuta inequality – the operator inequalities .