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).