Bounding the Frobenius norm of a q-deformed commutator

For two n × complex matrices A and B , we define the q -deformed commutator as [ ] : = − for a real parameter . In this paper, investigate generalization of Böttcher-Wenzel inequality which gives sharp upper bound (Frobenius) norm commutator. our generalisation, bounds on This can be studied in different scenarios: firstly general matrices, secondly traceless matrices. both scenarios, partial answers conjectures are given positive negative particular, denoting Frobenius by | F when or is normal, prove following to true sharp: 2 ≤ ( 1 + ) Also, conjecture that same traceless. other generic scenarios scenario All supported with numerics proved