We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We identify the C*-envelopes of certain quotients of tensor algebras over C*-correspondences.
1.Arveson, W., Subalgebras of C*-algebras, Acta Math.123 (1969), 141–224.CrossRefGoogle Scholar
2
2.Blecher, D., Muhly, P. and Paulsen, V., Categories of operator modules (Morita equivalence and projective modules), Mem. Am. Math. Soc.143, no. 681 (2000).Google Scholar
3
3.Davidson, K., Nest algebras, Pitman Research Notes in Mathematics Series, vol. 191 (Longman Scientific and Technical, Essex, 1988).Google Scholar
4
4.Davis, C., Kahan, W. and Weinberger, W., Norm preserving dilations and their applications to optimal error bounds, SIAM J. Numer. Analysis19 (1982), 445–469.CrossRefGoogle Scholar
5
5.Gabriel, P. and Roiter, A., Representations of finite-dimensional algebras, in Algebra VIII, Encyclopaedia of Mathematical Sciences (Springer, 1992).Google Scholar
6
6.Hochschild, G., On the structure of algebras with nonzero radical, Bull. Am. Math. Soc.53 (1947), 369–377.CrossRefGoogle Scholar
7
7.Lance, E. C., Hilbert C*-modules—a toolkit for operator algebraists, London Mathematical Society Lecture Notes (Cambridge University Press, 1995).CrossRefGoogle Scholar
8
8.Muhly, P. S., A finite dimensional introduction to operator algebra, in Operator algebras and applications (ed. Katavolos, A.), pp. 313–354, NATO Adv. Sci. Inst. C, Math. Phys. Sci., vol. 495 (Kluwer, Dordrecht, 1997).Google Scholar
9
9.Muhly, P. and Solel, B., Tensor algebras over C*-correspondences (representations, dilations, and C*-envelopes), J. Funct. Analysis158 (1998), 389–457.CrossRefGoogle Scholar
10
10.Muhly, P. and Solel, B., On the Morita equivalence of tensor algebras, Proc. Lond. Math. Soc. (In the press.)Google Scholar
11
11.Pimsner, M., A class of C*-algebras generalizing both Cuntz–Krieger algebras and crossed products by ℤ, in Free probability theory (ed. Voiculescu, D.), Fields Institute Communications, vol. 12, pp. 189–212 (American Mathematical Society, Providence, RI, 1997).Google Scholar
12
12.Popescu, G., Isometric dilations for infinite sequences of noncommuting operators, Trans. Am. Math. Soc.316 (1989), 523–536.CrossRefGoogle Scholar
13
13.Popescu, G., Noncommuting disc algebras and their representations, Proc. Am. Math. Soc.124 (1996), 2137–2148.CrossRefGoogle Scholar
14
14.Rieffel, M., Induced representations of C*-algebras, Adv. Math.13 (1974), 176–257.CrossRefGoogle Scholar
15
15.Solel, B., Operator algebras over C*-correspondences, in Operator algebras and applications (ed. Katavolos, A.), pp. 429–448, NATO Adv. Sci. Inst. C, Math. Phys. Sci., vol. 495 (Kluwer, Dordrecht, 1997).Google Scholar