Norm inequalities related to matrix commutators involving matrix functions

Kan, Osman; Solak, Süleyman

doi:10.1142/s1793557120400069

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2022

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Cited by 2 publications

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“…Since the proof of the original inequality, the result has been generalised using other norms (notably among them, the Schatten-p norm) of the commutators and other cases [10,11,12,13,14,15,16,17,18,19,20,21,22,23]. See [14] and [19] for a review of the history of this problem.…”

Section: Introductionmentioning

confidence: 99%

Bounding the Frobenius norm of a q-deformed commutator

Chruściński¹,

Kimura²,

Ohno³

et al. 2022

Preprint

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For two n × n complex matrices A and B, we define the q-deformed commutator as [ A, B ] q := AB − qBA for a real parameter q. In this paper, we investigate a generalization of the Böttcher-Wenzel inequality which gives the sharp upper bound of the (Frobenius) norm of the commutator. In our generalisation, we investigate sharp upper bounds on the q-deformed commutator. This generalization can be studied in two different scenarios: firstly bounds for general matrices, and secondly for traceless matrices. For both scenarios, partial answers

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