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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - D. S. Kalyuzhnyi
TI  - The von Neumann inequality for linear matrix functions of several variables
JO  - Matematičeskie zametki
PY  - 1998
SP  - 218
EP  - 223
VL  - 64
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a7/
LA  - ru
ID  - MZM_1998_64_2_a7
ER  - 
%0 Journal Article
%A D. S. Kalyuzhnyi
%T The von Neumann inequality for linear matrix functions of several variables
%J Matematičeskie zametki
%D 1998
%P 218-223
%V 64
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a7/
%G ru
%F MZM_1998_64_2_a7
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/

[1] Von Neumann J., “Eine Spectraltheorie für allgemeine Operatoren eines unitären Raumes”, Math. Nachr., 4 (1951), 258–281 | MR | Zbl

[2] Ando T., “On a pair of commutative contractions”, Ann. of Math. (2), 24 (1963), 88–90 | MR | Zbl

[3] Varopoulos N. Th., “On an inequality of von Neumann and an application of the metric theory of tensor products to operator theory”, J. Funct. Anal., 16 (1974), 83–100 | DOI | MR | Zbl

[4] Arveson W. B., “Subalgebras of $C^*$-algebras”, Acta Math., 123 (1969), 141–224 | DOI | MR | Zbl

[5] Kalyuzhniy D., “Multiparameter passive scattering linear stationary dynamic systems (discrete case)”, Mark Krein International Conference “Operator theory and applications”, Abstracts (Odessa, August 18–22, 1997), Odessa, 1997

[6] Sekevalfi-Nad B., Foyash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970

[7] Arveson W. B., “Subalgebras of $C^*$-algebras, II”, Acta Math., 128 (1972), 271–308 | DOI | MR | Zbl

[8] Szökefalvi-Nagy B., “Sur les contractions de l'espace de Hilbert”, Acta Sci. Math. (Szeged), 15 (1953), 87–92 | MR

[9] Stinespring W., “Positive functions on $C^*$-algebras”, Proc. Amer. Math. Soc., 6 (1955), 211–216 | DOI | MR | Zbl

[10] Parrott S., “Unitary dilations for commuting contractions”, Pacific J. Math., 34 (1970), 481–490 | MR | Zbl

[11] Takesaki M., Theory of Operator Algebras, V. 1, Springer, New York–Heidelberg–Berlin, 1979

[12] Shvarts L., Analiz, T. 2, Mir, M., 1972