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Moussounda Mouanda, J. (2021) On Kadison’s Similary Problem for Homomorphism of the Algebra of Complex Polynomials. Advances in Pure Mathematics, 11, 755-770.
https://doi.org/10.4236/apm.2021.119050

has been cited by the following article:

• TITLE: On Von Neumann’s Inequality for Matrices of Complex Polynomials

  AUTHORS: Joachim Moussounda Mouanda

  KEYWORDS: Fourier Coefficients, Operator Theory, Polynomials

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.11 No.4, December 10, 2021

  ABSTRACT: We prove that every matrix F∈Mk (Pn) is associated with the smallest positive integer d (F)≠1 such that d (F)‖F‖∞ is always bigger than the sum of the operator norms of the Fourier coefficients of F. We establish some inequalities for matrices of complex polynomials. In application, we show that von Neumann’s inequality holds up to the constant 2n for matrices of the algebra Mk (Pn).