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In this paper we shall give an affirmative solution to a problem, posed by Berger, Coburn and Lebow, for ${{C}^{*}}$-algebras on Hardy submodules.
[1]Ahern, P. R. and Clark, D. N., Invariant subspaces and analytic continuation in several variables. J. Math. Mech. 19(1969/70), 963–969.Google Scholar
[2]
[2]Agrawal, O. P., Clark, D. N. and Douglas, R. G., Invariant subspaces in the polydisk. Proc. J. Math. 121 (1986), 1–11.Google Scholar
[3]
[3]Berger, C. A., Coburn, L. A. and Lebow, A., Representation and index theory for C*-algebras generated by commuting isometries. J. Funct. Anal. 27 (1978), 51–99.Google Scholar
[4]
[4]Douglas, R. G. and Paulsen, V. I., Hilbert modules over function algebras. Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, Harlow, 1989.Google Scholar
[5]
[5]Douglas, R. G. and Yang, R., Operator theory in the Hardy space over the bidisk (I). Integral Equations Operator Theory 38 (2000), 207–221.Google Scholar
[6]
[6]Guo, K. and Yang, R., The core functions of submodules over the bidisk, preprint.Google Scholar
[7]
[7]Izuchi, K., Unitarily equivalence of invariant subspaces in the polydisk. Pacific J. Math. 130 (1987), 351–358.Google Scholar
[8]
[8]Izuchi, K., Invariant subspaces on a torus. lecture notes (1998), unpublished.Google Scholar
[9]
[9]Izuchi, K., Nakazi, T. and Seto, M., Backward shift invariant subspaces on a torus II, preprint.Google Scholar
[10]
[10]Paulsen, V. I., Rigidity Theorems in Spaces of Analytic Functions. Proc. Symp. Pure Math. 51, Part 1 (1990) 347–355.Google Scholar
[11]
[11]Rudin, W., Function theory in polydiscs, Benjamin, New York, 1969.Google Scholar
[12]
[12]Yang, R., BCL index and Fredholm tuples Proc. Amer.Math. Soc. 127 (1999), 2385–2393.Google Scholar
[13]
[13]Yang, R., The Berger-Shaw theorem in the Hardy module over the bidisk. J. Operator Theory 42 (1999), 379–404.Google Scholar
[14]
[14]Yang, R., Operator theory in the Hardy space over the bidisk (II). Integral Equations Operator Theory 42(2002) 99–124.Google Scholar
[15]
[15]Yang, R., Operator theory in the Hardy space over the bidisk (III). J. Funct. Anal. 186(2001) 521–545.Google Scholar
[16]
[16]Yang, R., On two variable Jordan blocks, preprint.Google Scholar
[17]
[17]Yang, R., Beurling's phenomenon in two variables, preprint.Google Scholar