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Multiplication operators on sobolev disk algebra

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Abstract

In this paper, we study the algebra consisting of analytic functions in the Sobolev space W2,2(D) (D is the unit disk), called the Sobolev disk algebra, explore the properties of the multiplication operators Mf on it and give the characterization of the commutant algebra A′(M f) of M f. We show that A′(M f) is commutative if and only if M* f is a Cowen-Douglas operator of index 1.

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References

  1. Dixmier, J., Foiaç, C., Surle spectre ponctuel d’un opératear, in Colloq. Math. János Bolyai. 5, Hilbert Space Operators and Operator Algebras, Amsterdam-London: North Holland Publ. Co, 1972, 127–133.

    Google Scholar 

  2. Herrero, D. A., Taylor, T. J., Wang, Z. Y., Variation of the point spectrum under compact perturbations, Operator Theory: Advances and Applications, 1988, 32: 113–158.

    MathSciNet  Google Scholar 

  3. Wang, Z. Y., Multiplication Operator on Sobolev Space (in Chinese), Beijing: Guo Fang Gong Ye Publishing House, 1992, 11670–1170.

    Google Scholar 

  4. Jiang, C. L., Wang, Z. Y., A class of strongly irreducible operators with nice property, J. Operator Theory, 1996, 36: 3–19.

    MATH  MathSciNet  Google Scholar 

  5. Jiang, C. L., Wang, Z. Y., Strongly irreducible operators on Hilbert space, x03C0;-Pitman Research Notes in Mathematics Series 389, London: Longman, 1998.

    Google Scholar 

  6. Adams, R. A., Sobolev Spaces, New York-San Francisco-London: Academic Press, 1975.

    MATH  Google Scholar 

  7. Lambert, A., Strictly cyclic operator algebra, Pacific J. Math., 1971, 38: 717–766.

    MathSciNet  Google Scholar 

  8. Rudin, W., Real And Complex Analysis, New york: McGraw-Hill Book Company, 1974.

    MATH  Google Scholar 

  9. Conway, J. B, Herrero, D. A., Morrel, B. B., Completing the Riesz-Dunford Functional Calculus, Memoirs of AMS, Vol. 82, No. 417, Providence: Amer. Math. Soc., 1989.

    Google Scholar 

  10. Cowen, M. J., Douglas, R. G., Complex geometry and operator theory, Bull. Amer. Math. Soc., 1977, 83: 131–133.

    Article  MATH  MathSciNet  Google Scholar 

  11. Griffiths, P., Algrebaic Curves (in Chinese), Beijing: Publishing House of Beijing University, 1985.

    Google Scholar 

  12. Jiang, C. L., Similarity classification of Cowen-Douglas operators, Canad. J. Math., 2004, 56: 742–775.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, East China University of Science and Technology, 200237, Shanghai, China

    Wang Zongyao & Liu Yiqiang

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  1. Wang Zongyao
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  2. Liu Yiqiang
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Correspondence to Wang Zongyao.

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Wang, Z., Liu, Y. Multiplication operators on sobolev disk algebra. Sci. China Ser. A-Math. 48, 1395–1410 (2005). https://doi.org/10.1360/022004-28

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