American Journal of Computational Mathematics

Volume 11, Issue 4 (December 2021)

ISSN Print: 2161-1203   ISSN Online: 2161-1211

Google-based Impact Factor: 1.05  Citations  

On Von Neumann’s Inequality for Matrices of Complex Polynomials

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DOI: 10.4236/ajcm.2021.114019    217 Downloads   988 Views  Citations

ABSTRACT

We prove that every matrix FMk (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).


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Mouanda, J. (2021) On Von Neumann’s Inequality for Matrices of Complex Polynomials. American Journal of Computational Mathematics, 11, 289-303. doi: 10.4236/ajcm.2021.114019.

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