Geodesic
Positive-Defininte Functions on Free Semigroups
Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 887-896

Voir la notice de l'article provenant de la source Cambridge University Press

An extension of the Naimark dilation theorem [N], [SzF2] to positive-definite functions on free semigroups is given. This is used to extend the operatorial trigonometric moment problem [A] to a non-commutative setting and to characterize the classes Cρ (ρ > 0) of all n-tuples of operators that have a p-isometric dilation (see [SzF2] for the case n = 1). It is also shown that Cρ ⊂ Cρ′ and Cρ ≠ Cρ′ for 0 < ρ < ρ′ < ∞.The von Neumann inequality [vN], [Po2] is extended to the classes Cp . This is used to prove that any element in Cρ is simultaneously similar to an element in C 1.
DOI : 10.4153/CJM-1996-045-3
Mots-clés : 47A20, 47A45, 47A57 
Popescu, Gelu. Positive-Defininte Functions on Free Semigroups. Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 887-896. doi: 10.4153/CJM-1996-045-3
@article{10_4153_CJM_1996_045_3,
     author = {Popescu, Gelu},
     title = {Positive-Defininte {Functions} on {Free} {Semigroups}},
     journal = {Canadian journal of mathematics},
     pages = {887--896},
     year = {1996},
     volume = {48},
     number = {4},
     doi = {10.4153/CJM-1996-045-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-045-3/}
}
TY  - JOUR
AU  - Popescu, Gelu
TI  - Positive-Defininte Functions on Free Semigroups
JO  - Canadian journal of mathematics
PY  - 1996
SP  - 887
EP  - 896
VL  - 48
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-045-3/
DO  - 10.4153/CJM-1996-045-3
ID  - 10_4153_CJM_1996_045_3
ER  - 
%0 Journal Article
%A Popescu, Gelu
%T Positive-Defininte Functions on Free Semigroups
%J Canadian journal of mathematics
%D 1996
%P 887-896
%V 48
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-045-3/
%R 10.4153/CJM-1996-045-3
%F 10_4153_CJM_1996_045_3

[A] Akhiezer, N.I., The classical moment problem, Edinburg, Scotland: Olivier and Boyd (1965). Google Scholar

[Cu] Cuntz, J., Simple C*-algebras generated by isometries, Comm. Math., Phys. 57(1977), 173–185. Google Scholar

[E] Evans, D.E., On On, Publ. Res. Int. Math., Sci. 16(1980), 915–927. Google Scholar

[N] Naimark, M.A., Positive definite operator functions on a commutative group, Bulletin Acad. Sci., URSS 7(1943), 237–244. Google Scholar

[PS] Parthasarathy, K.R. and Schmidt, K., Positive-definite kernels, continuous tensor products and central limit theorems of probability theory, Lecture Notes in Mathematics, Springer, Berlin 272 1972. Google Scholar

[P] Paulsen, V.I., Every completely polynomially bounded operator is similar to a contraction, J. Funct., Anal. 55(1984), 1–17. Google Scholar

[Pol] Popescu, G., Isometric dilations for infinite sequences of noncommuting operators, Trans. Amer. Math., Soc. 316(1989), 523–536. Google Scholar

[Po2] Popescu, G., Von Neumann inequality for (B﹛H)n)x, Math., Scand. 68(1991), 292–304. Google Scholar

[Po3] Popescu, G., Functional calculus for noncommuting operators, Michigan Math., J. 42(1995), 345–356. Google Scholar

[Po4] Popescu, G., Non-commutative disc algebras and their representations, Proc. Amer. Math. Soc, to appear. Google Scholar

[S] Stinespring, W.F., Positive functions on C* -algebras, Proc. Amer. Math., Soc. 6(1955). Google Scholar

[SzFl] -Nagy, B.Sz.,Foias, C., Similitude des operators de classe Cp a des contractions, C. R. Acad. Sci. Paris, serie, A, 264(1967), 1063–1065. Google Scholar

[SzF2] -Nagy, B.Sz., Harmonic analysis on operators on Hilbert space, North—Holland, Amsterdam (1970). Google Scholar

[vN] von, J. Neumann, Eine Spectraltheorie fur allgemeine Operatoren eines unitaren Raumes, Math., Nachr. 4(1951), 258–281. Google Scholar

Cité par Sources :