Noncommutative Disc Algebras for Semigroups

Davidson, Kenneth R. ; Popescu, Gelu

Canadian journal of mathematics, Tome 50 (1998) no. 2, pp. 290-311

Détail

DOI : 10.4153/CJM-1998-015-5

Mots-clés : 47D25

Bibliographie

[1] 1. Agler, J., The Arveson extension theorem and coanalytic models. Integral Equations Operator Theory 5(1982), 608–631. Google Scholar

[2] 2. Akhiezer, N.I., The classical moment problem. Olivier and Boyd, Edinburgh, Scotland, 1965. Google Scholar

[3] 3. Arveson, W.B., Subalgebras of C*-algebras. Acta Math. 123(1969), 141–224. Google Scholar

[4] 4. Arveson, W.B., Continuous analogues of Fock space. Mem. Amer. Math. Soc. (409) 80(1989). Google Scholar

[5] 5. Blecher, D.P. and Paulsen, V.I., Explicit construction of universal operator algebras and applications to polynomial factorization. Proc. Amer.Math. Soc. 112(1991), 839–850. Google Scholar

[6] 6. Bunce, J.W., Models for n-tuples of noncommuting operators. J. Func. Anal. 57(1984), 21–30. Google Scholar

[7] 7. Coburn, L.A., The CŁ–algebra generated by an isometry, I. Bull. Amer.Math. Soc. 13(1967), 722–726. Google Scholar

[8] 8. Cuntz, J., Simple CŁ–algebras generated by isometries. Comm.Math. Phys. 57(1977), 173–185. Google Scholar

[9] 9. Cuntz, J., K-theory for certain CŁ–algebras. Ann. Math. 113(1981), 181–197. Google Scholar

[10] 10. Davidson, K.R., C*-algebras by example. Fields Inst. Monographs 6, Amer. Math. Soc., Providence, RI, 1996. Google Scholar

[11] 11. Davidson, K.R. and Pitts, D.R., Invariant subspaces and hyperreflexivity for free semigroup algebras. Proc. London Math. Soc., to appear. Google Scholar

[12] 12. Davidson, K.R., The algebraic structure of non-commutative analytic Toeplitz algebras. Math. Ann., to appear. Google Scholar

[13] 13. Dinh, H.T., Discrete product systems and their C*–algebras. J. Funct. Anal. 102(1991), 1–34. Google Scholar

[14] 14. Dinh, H.T., On generalized Cuntz C*–algebras. J. Operator Theory 30(1993), 123–135. Google Scholar

[15] 15. Douglas, R.G., On the C*-algebra of a one-parameter semigroup of isometries. Acta Math. 128(1972), 143–152. Google Scholar

[16] 16. Frahzo, A., Models for non-commuting operators. J. Funct.Anal. 48(1982), 1–11. Google Scholar

[17] 17. Laca, M. and Raeburn, I., Semigroup crossed products and the Toeplitz algebras of non-abelian groups. J. Funct. Anal. 139(1996), 415–440. Google Scholar

[18] 18. Laca, M., Purely infinite simple Toeplitz algebras. Preprint, 1997. Google Scholar

[19] 19. Mlak, W., Unitary dilations in case of ordered groups. Ann. Polon. Math. 17(1960), 321–328. Google Scholar

[20] 20. Nica, A.,C*-algebras generated by isometries andWiener–Hopf operators. J. Operator Theory 27(1992), 17–52. Google Scholar

[21] 21. Paulsen, V.I., Completely bounded maps and dilations. Pitman Res. NotesMath. Ser. 146, Longman Sci. Tech., Harlow, 1986. Google Scholar

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

[23] 23. Popescu, G., Von Neumann inequality for (B(H)n. 1. Math. Scand. 68(1991), 292–304. Google Scholar

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

[25] 25. Popescu, G., Non-commutative disc algebras and their representations. Proc. Amer. Math. Soc. 124(1996), 2137–2148. Google Scholar

[26] 26. Popescu, G., Positive-definite functions on free semigroups. Can. J. Math. 48(1996), 887–896. Google Scholar

[27] 27. Popescu, G., Noncommutative joint dilations and free product operator algebras. Pacific J. Math, to appear. Google Scholar

[28] 28. Popescu, G., Positive definite kernels on free product semigroups and universal algebras. Math. Scand., to appear. Google Scholar

[29] 29. Rudin, W., Fourier Analysis on Groups. Interscience Publishers, New York, 1962. Google Scholar

[30] 30. Stinespring, W.F., Positive functions on C*-algebras. Proc. Amer. Math. Soc. 6(1955), 211–216. Google Scholar

[31] 31. Nagy, B.Sz., Sur les contractions de l’espace de Hilbert. Acta. Sci. Math. (Szeged) 15(1953), 87–92. Google Scholar

[32] 32. Nagy, B.Sz., Transformations de l’espace de Hilbert, fonctions de type positif sur un groupe. Acta. Sci.Math. (Szeged) 15(1954), 104–114. Google Scholar

[33] 33. Nagy, B.Sz. and Foias, C., Harmonic analysis of operators on Hilbert space. Akademiai Kaidó, Budapest, 1970. Google Scholar

[34] 34. von Neumann, J., Eine spektraltheorie für allgemeine operatoren eines unitären raumes. Math. Nachr. 4(1951), 49–131. Google Scholar