Determine the least constant c∈R such that, for every n∈N and all contractions A,B,C∈ M_n(C), one has |A+B+C|≤ cI_n+|A|+|B|+|C|, where |X|=(X^X)^1/2. The cited preprint claims that the optimal constant is c=frac34, and that this value cannot be replaced by any smaller constant.

Open problems of Audenaert–Kittaneh, Bourin, and Lee

The entry collects questions recorded by Audenaert and Kittaneh, including problems attributed to Bourin and Lee. The underlying list includes extremal inequalities for operators, Schatten norms, singular values, and positive matrices.

Known results

Lee proved the general unitarily invariant norm bound with constant $c=\sqrt{2}$ and showed it is optimal.
Lee’s sharper Frobenius-norm constant is $c=\sqrt{(1+\sqrt{2})/2}$ , but the corresponding general question was recorded as open.
A preprint dated January 10, 2024, claimed the Audenaert–Kittaneh Schatten-norm conjecture for $1<p\leq 2$ , with the reverse inequality for $2\leq p<\infty$ claimed by duality.

September 17, 2026 claimed solutions

Aouichaoui and Lee’s preprint claims solutions to multiple listed questions, including a sharp three-contraction inequality and an eigenvalue inequality for symmetric moduli. Related 2026 preprints claim the negative-exponent complementary McCarthy range and a sharp Lee-type concave-function inequality. These claims are unverified.

Current status (as of September 2026): Several questions have claimed solutions in recent unrefereed preprints, while independent verification and the status of the remaining listed problems are unresolved.

Open problems of Audenaert–Kittaneh, Bourin, and Lee

Primary source

Additional references

Progress summary

Solutions 0