Geodesic
The von Neumann inequality for linear matrix functions of several variables
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 218-223

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It is proved that there exist three commuting contractions in Hilbert space and a linear homogeneous matrix function of three independent variables for which the generalized von Neumann inequality is not satisfied. 
@article{MZM_1998_64_2_a7,
     author = {D. S. Kalyuzhnyi},
     title = {The von {Neumann} inequality for linear matrix functions of several variables},
     journal = {Matemati\v{c}eskie zametki},
     pages = {218--223},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a7/}
}
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D. S. Kalyuzhnyi. The von Neumann inequality for linear matrix functions of several variables. Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 218-223. http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a7/