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Hardy Algebras Associated with W*-Correspondences (Point Evaluation and Schur Class Functions)

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References

  1. J. Agler and J. McCarthy, Pick interpolation and Hilbert function spaces. Graduate Studies in Mathematics, vol. 44. Amer. Math. Soc., Providence (2002).

    Google Scholar 

  2. D. Alpay, P. Bruinsma, A. Dijksma and H. de Snoo, Interpolation problems, extensions of symmetric operators and reproducing kernel spaces II, Int. Eq. Oper. Thy. 14 (1991), 465–500.

    Article  Google Scholar 

  3. D. Alpay, P. Bruinsma, A. Dijksma and H. de Snoo, Interpolation problems, extensions of symmetric operators and reproducing kernel spaces II (missing section 3), Int. Eq. Oper. Thy. 15 (1992), 378–388.

    Article  Google Scholar 

  4. D. Alpay, P. Dewilde and H. Dym, Lossless inverse scattering and reproducing kernels for upper triangular operators, Operator Theory: Adv. Appl., Birkhäuser Verlag, Basel 47 (1990), 61–133.

    Google Scholar 

  5. D. Alpay, A Dijksma and Y. Peretz, Nonstationary analogues of the Herglotz representation theorem: the discrete case, J. Funct. Anal. 66 (1999), 85–129.

    Article  Google Scholar 

  6. C. Anantharaman-Delaroche, On completely positive maps defined by an irreducible correspondence, Canad. Math. Bull. 33 (1990), 434–441.

    Google Scholar 

  7. M. Anoussis, Interpolating operators in nest algebras, Proc. Amer. Math. Soc. 114 (1992), 707–710.

    Google Scholar 

  8. A. Arias and G. Popescu, Noncommrutative interpolation and Poison transforms. Israel J. Math. 115 (2000), 205–234.

    Google Scholar 

  9. Wm. Arveson, Interpolation problems in nest algebras, J. Funct. Anal. 3 (1975), 208–233.

    Article  Google Scholar 

  10. W.B. Arveson, Continuous analogues of Fock space, Mem. Amer. Math. Soc. 80 (1989).

    Google Scholar 

  11. M. Baillet, Y. Denizeau and J.-F. Havet, Indice d’une esperance conditionelle, Comp. Math. 66 (1988), 199–236.

    Google Scholar 

  12. J. Ball, Linear systems, operator model theory and scattering: multivariable generalizations, in Operator Theory and its applications (Winnipeg, 1998) (Ed. A.G. Ramm, P.N. Shivakumar and A.V. Strauss), Fields Inst. Comm. vol. 25, Amer. Math. Soc., Providence, 2000, 151–178.

    Google Scholar 

  13. J. Ball and I. Gohberg, A commnutant lifting theorem for triangular matrices with diverse applications, Integral Equat. Operator Theory 8 (1985), 205–267.

    Article  Google Scholar 

  14. J. Ball, T. Trent and V. Vinnikov, Interpolation and commrutant lifting for multipliers on reproducing kernel Hilbert spaces. Preprint.

    Google Scholar 

  15. J. Ball and V. Vinnikov, Functional models for representations of the Cuntz algebra. Preprint.

    Google Scholar 

  16. S.D. Barreto, B.V.R. Bhat, V. Liebscher and M. Skeide, Type I product systems of Hilbert modules, to appear in J. Functional Anal.

    Google Scholar 

  17. H. Bercovici, Operator theory and arithmetic in H∞. Mathematical Surveys and Monographs, 26. American Mathematical Society, Providence, RI, 1988.

    Google Scholar 

  18. M.D. Choi, Completely positive linear maps on complex matrices, Lin. Alg. Appl. 10 (1975), 285–290.

    Article  Google Scholar 

  19. K. Davidson and D. Pitts, The algebraic structure of non-commutative analytic Toeplitz algebras, Math. Ann. 311 (1998), 275–303.

    Article  Google Scholar 

  20. H. Dym, J-contractive matrix finctions. reproducing kernel Hilbert spaces and interpolation. CBMS Regional Conference Ser. Math. 71. Amer. Math. Soc., Providence, RI, 1989. x+147 pp.

    Google Scholar 

  21. P. Gabriel, Unzerlegbare Darstellungen I, Manuscr. Math. 6 (1972), 71–103.

    Article  Google Scholar 

  22. P. Gabriel and A.V. Roiter, Representations of Finite-Dimensional Algebras, Algebra VIII, Encyclopaedia of Mathematical Sciences, Vol. 73, Springer-Verlag, 1991.

    Google Scholar 

  23. G. Hochschild, On the structure of algebras with nonzero radical, Bull. Amer. Math. Soc. 53 (1947), 369–377.

    Google Scholar 

  24. E.G. Katsoulis, R.L. Moore and T.T. Trent, Interpolation in nest algebras and applications to operator corona theorems, J. Operator Th. 29 (1993), 115–123.

    Google Scholar 

  25. D. Kribs and S. Power, Free semigroupoid algebras, Preprint.

    Google Scholar 

  26. E.C. Lance, Some properties of nest algebras, Proc. London Math. Soc. (3) 19 (1969), 45–68.

    Google Scholar 

  27. E.C. Lance, Hilbert C*-modules, A toolkit for operator algebraists, London Math. Soc. Lecture Notes series 210 (1995). Cambridge Univ. Press.

    Google Scholar 

  28. M. McAsey and P.S. Muhly, Representations of non-self-adjoint crossed products, Proc. London Math. Soc. 47 (1983), 128–144.

    Google Scholar 

  29. J. Mingo, The correspondence associated to an inner completely positive map, Math. Ann. 284 (1989), 121–135.

    Article  Google Scholar 

  30. P.S. Muhly, A finite-dimensional introduction to operator algebra in Operator algebras and applications (Samos. 1996), 313–354, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 495, Kluwer Acad. Publ., Dordrecht, 1997.

    Google Scholar 

  31. P.S. Muhly and B. Solel, Tensor algebras over C*-correspondences (Representations, dilations and C*-envelopes), J. Funct. Anal. 158 (1998), 389–457.

    Article  Google Scholar 

  32. P.S. Muhly and B. Solel, Tensor algebras, induced representations, and the Wold decomposition, Canad. J. Math. 51 (1999), 850–880.

    Google Scholar 

  33. P.S. Muhly and B. Solel, Quantum Markov processes (correspondences and dilations), Int. J. Math. 13 (2002), 863–906.

    Article  Google Scholar 

  34. P.S. Muhly and B. Solel, The curvature and index of completely positive maps, Proc. London Math. Soc. 87 (2003), 748–778.

    Article  Google Scholar 

  35. P.S. Muhly and B. Solel, Hardy algebras. W*-correspondences and interpolation theory, to appear in Math. Ann.

    Google Scholar 

  36. P.S. Muhly and B. Solel, On canonical models for representations of Hardy algebras. In preparation.

    Google Scholar 

  37. P.S. Muhly and B. Solel, Schur class operator functions associated with a W*-correspondence. In preparation.

    Google Scholar 

  38. P.S. Muhly, M. Skeide and B. Solel, Representations of Ba(E), commutants of von Neumann bimodules, and product systems of Hilbert modules. In preparation.

    Google Scholar 

  39. B. Sz.-Nagy and C. Foias, Analyse Harmonique des Opérateurs de l’espace de Hilbert, Akademiai Kiado (1966).

    Google Scholar 

  40. W. Paschke, Inner product modules over B*-algebras, Trans. Amer. Math. Soc. 182 (1973), 443–468.

    Google Scholar 

  41. J. Peters, Semi-crossed products of C*-algebras, J. Funct. Anal. 59 (1984), 498–534.

    Article  Google Scholar 

  42. M. Pimsner, A class of C*-algebras generalizing both Cuntz-Krieger algebras and crossed products by ℤ, in Free Probability Theory, D. Voiculescu, Ed., Fields Institute Comm. 12, 189–212, Amer. Math. Soc., Providence, 1997.

    Google Scholar 

  43. S. Popa, Correspondences, Preprint (1986).

    Google Scholar 

  44. G. Popescu, Characteristic functions for infinite sequences of noncommuting operators, J. Oper. Theory 22 (1989), 51–71.

    Google Scholar 

  45. G. Popescu, von Neumann inequality for B(ℌn) 1 , Math. Scand. 68 (1991), 292–304.

    Google Scholar 

  46. G. Popescu, Functional calculus for noncommuting operators, Mich. Math. J. 42 (1995), 345–356.

    Article  Google Scholar 

  47. G. Popescu, Commutant lifting, tensor algebras and functional calculus, Proc. Edinburg Math. Soc. 44 (2001), 389–406.

    Article  Google Scholar 

  48. M.A. Rieffel, Induced representations of C*-algebras, Adv. in Math. 13 (1974), 176–257.

    Article  Google Scholar 

  49. D. Sarason, Generalized interpolation in H∞, Trans. Amer. Math. Soc. 127 (1967), 179–203.

    Google Scholar 

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Muhly, P.S., Solel, B. (2005). Hardy Algebras Associated with W*-Correspondences (Point Evaluation and Schur Class Functions). In: Alpay, D., Vinnikov, V. (eds) Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations. Operator Theory: Advances and Applications, vol 157. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7303-2_8

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