7 papers
On interrelations among different versions of a Heron type mean and commutativity in -Algebras
Lajos Molnár, Teng Zhang
The extension of the concept of a mean of positive real numbers to noncommutative settings, e.g., for Hilbert space operators, is a widely studied question. For example, in quantum…
Plank theorems, Gaussian probabilistic estimates and Rump's 100 Euro conjecture
Teng Zhang
We prove Rump's 100-euro conjecture by deriving a weighted affine escape theorem from Ball's plank theorem in [Invent. Math. \textbf{104} (1991)]. More precisely, let $\mathbb{K}\i…
On a conjecture of -Aluthge transforms and Hilbert--Schmidt self-commutators
Teng Zhang
Let be a complex square matrix, and write its polar decomposition as . For , the -Aluthge transform of is defined by I…
Operator symmetric moduli and sharp triangle inequalities
Teng Zhang
We compare the usual operator modulus with two symmetrized variants, the arithmetic symmetric modulus and the quadratic symmetric modulus. For every unitarily invariant norm, we de…
Trace arithmetic-- inequality
Teng Zhang
Let be a unital -algebra equipped with a faithful tracial positive linear functional . Denote by its positive cone. For and $A,B\in\…
Bourin-type inequalities for -measurable operators in fully symmetric spaces
Teng Zhang
Let be a semifinite von Neumann algebra, where denotes the algebra of all bounded linear operators on a Hilbert space $\mathcal…