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On the Berger-Coburn-Lebow Problem for Hardy Submodules

Published online by Cambridge University Press:  20 November 2018

Michio Seto
Michio Seto*
Affiliation:
Mathematical Institute Tohoku University Sendai 980-8578 Japan, e-mail: [email protected]
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Abstract

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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.

Keywords

47B3847B35Hardy submodules
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 456 - 467
Copyright
Copyright © Canadian Mathematical Society 2004

References

[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] 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] 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] 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] 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] Guo, K. and Yang, R., The core functions of submodules over the bidisk, preprint.Google Scholar
[7] Izuchi, K., Unitarily equivalence of invariant subspaces in the polydisk. Pacific J. Math. 130 (1987), 351–358.Google Scholar
[8] Izuchi, K., Invariant subspaces on a torus. lecture notes (1998), unpublished.Google Scholar
[9] Izuchi, K., Nakazi, T. and Seto, M., Backward shift invariant subspaces on a torus II, preprint.Google Scholar
[10] Paulsen, V. I., Rigidity Theorems in Spaces of Analytic Functions. Proc. Symp. Pure Math. 51, Part 1 (1990) 347–355.Google Scholar
[11] Rudin, W., Function theory in polydiscs, Benjamin, New York, 1969.Google Scholar
[12] Yang, R., BCL index and Fredholm tuples Proc. Amer.Math. Soc. 127 (1999), 2385–2393.Google Scholar
[13] Yang, R., The Berger-Shaw theorem in the Hardy module over the bidisk. J. Operator Theory 42 (1999), 379–404.Google Scholar
[14] Yang, R., Operator theory in the Hardy space over the bidisk (II). Integral Equations Operator Theory 42(2002) 99–124.Google Scholar
[15] Yang, R., Operator theory in the Hardy space over the bidisk (III). J. Funct. Anal. 186(2001) 521–545.Google Scholar
[16] Yang, R., On two variable Jordan blocks, preprint.Google Scholar
[17] Yang, R., Beurling's phenomenon in two variables, preprint.Google Scholar