Isometric dilations of non-commuting finite rank n-tuples

Canadian Journal of Mathematics

Volumn 53, Issue 3, 2001, Pages 506-545

  Davidson, Kenneth R ^a   Kribs, David W ^a   Shpigel, Miron E ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b Mitra Imaging Inc   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035592653     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-2001-022-0     Document Type: Article

References (35)

1. A. Arias and G. Popescu, Factorization and reflexivity on Fock spaces. Integral Equations Operator Theory 23(1995), 268-286.
2. W. Arveson, Interpolation problems in nest algebras. J. Funct. Anal. 20(1975), 208-233.
3. _, Subalgebras of C*-algebras III: multivariable operator theory. Acta Math., to appear.
4. n]. preprint, 1998.
5. E. Azoff, C. K. Fong and F. Gilfeather, A reduction theory for nonself-adjoint operator algebras. Trans. Amer. Math. Soc. 224(1976), 351-366.
6. H. Bercovici, Hyper-reflexivity and the factorization of linear functionals. J. Funct. Anal. 158(1998), 242-252.
7. A. Beurling, On two problems concerning linear transformations in Hilbert space. Acta Math. 81(1949), 239-255.
8. O. Bratteli, P. Jorgensen, and G. L. Price, Endomorphisms of B(H). In: Quantization of nonlinear partial differential equations, (eds. W. Arveson et al), Proc. Symp. Pure Math. 59, Amer. Math. Soc., Providence, 1996, 93-138.
9. O. Bratteli and P. Jorgensen, Endomorphisms of B(H) II. J. Funct. Anal. 145 (1997), 323-373.
10. _, Iterated function systems and permutation representations of the Cuntz algebra. Mem. Amer. Math. Soc., to appear.
11. J. Bunce, Models for n-tuples of non-commuting operators. J. Funct. Anal. 57(1984), 21-30.
12. E. Christensen, Perturbations of operator algebras II. Indiana Univ. Math. J. 26(1977), 891-904.
13. J. Cuntz, Simple C*-algebras generated by isometries. Comm. Math. Phys. 57(1977), 173-185.
14. K. R. Davidson, The distance to the analytic Toeplitz operators. Illinois J. Math. 31(1987), 265-273.
15. K. R. Davidson and D. R. Pitts, Invariant subspaces and hyper-reflexivity for free semi-group algebras. Proc. London Math. Soc. 78(1999), 401-430.
16. _, The algebraic structure of non-commutative analytic Toeplitz algebras. Math. Ann. 311(1998), 275-303.
17. _, Nevanlinna-Pick Interpolation for non-commutative analytic Toeplitz algebras. Integral Equations Operator Theory 31(1998), 321-337.
18. J. Dyer, A. Pedersen and P. Porcelli, An equivalent formulation of the invariant subspace problem. Bull. Amer. Math. Soc. 78(1972), 1020-1023.
19. A. Frahzo, Models for non-commuting operators. J. Funct. Anal. 48(1982), 1-11.
20. _, Complements to models for non-commuting operators. J. Funct. Anal. 59(1984), 445-461.
21. S. Friedland, Simultaneous similarity of matrices. Adv. in Math. 50(1983), 189-265.
22. J. Glimm, Type IC*-algebras. Ann. of Math. 73(1961), 572-612.
23. D. W. Kribs, Factoring in non-commutative analytic Toeplitz algebras. J. Operator Theory. to appear.
24. D. W. Kribs, The curvature invariant of a non-commuting n-tuple. preprint, 2000.
25. M. Laca, Endomorphisms of B(H) and Cuntz algebras. J. Operator Theory 30(1993), 381-396.
26. G. Popescu, Isometric dilations for infinite sequences of noncommuting operators. Trans. Amer. Math. Soc. 316(1989), 523-536.
27. _, Multi-analytic operators and some factorization theorems. Indiana Univ. Math. J. 38(1989), 693-710.
28. 1. Math. Scand. 68(1991), 292-304.
29. _, Multi-analytic operators on Fock spaces. Math. Ann. 303(1995), 31-46.
30. _, Poisson transforms on some C*-algebras generated by isometries. J. Funct. Anal., to appear.
31. R. Powers, An index theory for semigroups of *-endomorphisms of B(H) and type II factors. Canad. J. Math. 40(1988), 86-114.
32. H. Radjavi and P. Rosenthal, Invariant subspaces. Ergebnisse der Math, und ihrer Grenz. 77, New York, Heidelberg, Berlin, Springer-Verlag, 1973.
33. D. Sarason, On spectral sets having connected complement. Acta Sci. Math. (Szeged) 26(1965), 289-299.
34. B. Sz. Nagy, and C. Foiaş, Harmonic analysis of operators on Hilbert space. North Holland Pub. Co., London, 1970.
35. J. Wermer, On invariant subspaces of normal operators. Proc. Amer. Math. Soc. 3(1952), 270-277.