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Noncommutative Disc Algebras for Semigroups

Published online by Cambridge University Press:  20 November 2018

Kenneth R. Davidson  and
Gelu Popescu
Kenneth R. Davidson
Affiliation:
Pure Mathematics Department University of Waterloo Waterloo, Ontario N2L 3G1, e-mail: [email protected]
Gelu Popescu
Affiliation:
Division of Mathematics and Statistics University of Texas at San Antonio San Antonio, TX 78249 USA, e-mail: [email protected]
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Abstract

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Keywords

47D25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 2 , 01 April 1998 , pp. 290 - 311
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Agler, J., The Arveson extension theorem and coanalytic models. Integral Equations Operator Theory 5(1982), 608–631.Google Scholar
2. Akhiezer, N.I., The classical moment problem. Olivier and Boyd, Edinburgh, Scotland, 1965.Google Scholar
3. Arveson, W.B., Subalgebras of C*-algebras. Acta Math. 123(1969), 141–224.Google Scholar
4. Arveson, W.B., Continuous analogues of Fock space. Mem. Amer. Math. Soc. (409) 80(1989).Google Scholar
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. Bunce, J.W., Models for n-tuples of noncommuting operators. J. Func. Anal. 57(1984), 21–30.Google Scholar
7. Coburn, L.A., The CŁ–algebra generated by an isometry, I. Bull. Amer.Math. Soc. 13(1967), 722–726.Google Scholar
8. Cuntz, J., Simple CŁ–algebras generated by isometries. Comm.Math. Phys. 57(1977), 173–185.Google Scholar
9. Cuntz, J., K-theory for certain CŁ–algebras. Ann. Math. 113(1981), 181–197.Google Scholar
10. Davidson, K.R., C*-algebras by example. Fields Inst. Monographs 6, Amer. Math. Soc., Providence, RI, 1996.Google Scholar
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. Davidson, K.R., The algebraic structure of non-commutative analytic Toeplitz algebras. Math. Ann., to appear.Google Scholar
13. Dinh, H.T., Discrete product systems and their C*–algebras. J. Funct. Anal. 102(1991), 1–34.Google Scholar
14. Dinh, H.T., On generalized Cuntz C*–algebras. J. Operator Theory 30(1993), 123–135.Google Scholar
15. Douglas, R.G., On the C*-algebra of a one-parameter semigroup of isometries. Acta Math. 128(1972), 143–152.Google Scholar
16. Frahzo, A., Models for non-commuting operators. J. Funct.Anal. 48(1982), 1–11.Google Scholar
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. Laca, M., Purely infinite simple Toeplitz algebras. Preprint, 1997.Google Scholar
19. Mlak, W., Unitary dilations in case of ordered groups. Ann. Polon. Math. 17(1960), 321–328.Google Scholar
20. Nica, A.,C*-algebras generated by isometries andWiener–Hopf operators. J. Operator Theory 27(1992), 17–52.Google Scholar
21. Paulsen, V.I., Completely bounded maps and dilations. Pitman Res. NotesMath. Ser. 146, Longman Sci. Tech., Harlow, 1986.Google Scholar
22. Popescu, G., Isometric dilations for infinite sequences of noncommuting operators. Trans. Amer.Math. Soc. 316(1989), 523–536.Google Scholar
23. Popescu, G., Von Neumann inequality for (B(H)n. 1. Math. Scand. 68(1991), 292–304.Google Scholar
24. Popescu, G., Functional calculus for noncommuting operators. Mich. J. Math. 42(1995), 345–356.Google Scholar
25. Popescu, G., Non-commutative disc algebras and their representations. Proc. Amer. Math. Soc. 124(1996), 2137–2148.Google Scholar
26. Popescu, G., Positive-definite functions on free semigroups. Can. J. Math. 48(1996), 887–896.Google Scholar
27. Popescu, G., Noncommutative joint dilations and free product operator algebras. Pacific J. Math, to appear.Google Scholar
28. Popescu, G., Positive definite kernels on free product semigroups and universal algebras. Math. Scand., to appear.Google Scholar
29. Rudin, W., Fourier Analysis on Groups. Interscience Publishers, New York, 1962.Google Scholar
30. Stinespring, W.F., Positive functions on C*-algebras. Proc. Amer. Math. Soc. 6(1955), 211–216.Google Scholar
31. Nagy, B.Sz., Sur les contractions de l’espace de Hilbert. Acta. Sci. Math. (Szeged) 15(1953), 87–92.Google Scholar
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. Nagy, B.Sz. and Foias, C., Harmonic analysis of operators on Hilbert space. Akademiai Kaidó, Budapest, 1970.Google Scholar
34. von Neumann, J., Eine spektraltheorie für allgemeine operatoren eines unitären raumes. Math. Nachr. 4(1951), 49–131.Google Scholar