We prove that von Neumann’s inequality holds for circulant contractions. We show that every complex polynomial over is associated to a constant such that von Neumann’s inequality can hold up to , for -tuples of commuting contractions on a Hilbert space. We characterise complex polynomials over in which . We introduce the properties of upper (or lower) complex triangular Toeplitz matrices. We show that von Neumann’s inequality holds for -tuples of upper (or lower) complex triangular Toeplitz contractions. We construct contractive homomorphisms.
"On von Neumann's inequality for complex triangular Toeplitz contractions." Rocky Mountain J. Math. 50 (1) 213 - 224, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.213