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On the unique finite (SI) decomposition of the Jordan operator ⊕ n i=1 S(θ) for certain inner function θ

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Abstract

In this paper, we have proven that for the Jordan blockS(θ) withS(θ) ∈ (SI), ⊕ n i=1 S(θ) =S(θ)(n)(n ≥ 1) has unique finite (SI) decomposition up to a similarity. As result, we obtain that ifV is a Volterra operator onH=L 2([0, 1]), thenV (n) has unique finite (SI) decomposition.

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References

  1. H. Bercovici, Operator Theory and Arithmetic inH ∞, Amer. Math. Soc. Providence RI, 1988.

    Google Scholar 

  2. B. Blackadar, K-Theory for Operator Algebras, MSRI Publications No.5, Springer-Verlag, 1986.

  3. Y. Cao, J. Fang and C. Jiang,K-group of Banach algebras and strongly irreducible decomposition of operators, (to appear).

  4. J.B. Conway, Subnormal Operators, π Pitman Advanced Publishing Program, Boston-London-Melbourne, 1981.

    Google Scholar 

  5. K.R. Davidson, Nest Algebras, Research notes in Mathematics 191, Longman Harlow-Essex, 1988.

    Google Scholar 

  6. J.B. Garnett, Bounded analytic functions, Academic Press, New York, 1981.

    Google Scholar 

  7. C.L. Jiang and Z.Y. Wang, Strongly Irreducible Operators on Hiblert Spaces, π Pitman Research Notes in Mathematics Series 389, Addison-Wesley-Longman Company, 1998

  8. A. Lambert, Strictly cyclic operator algebra, Pacific J. Math. 38 (1971), 717–726.

    Google Scholar 

  9. A.L. Leonardo, Stable range and approximation theorems inH ∞, Trans. Amer. Math. Soc. 327 (2) (1991), 815–832

    Google Scholar 

  10. M.A. Rieffel, Dimensionl and stable rank in theK-theory ofC *-Algebras, Proc. London Math. Soc. 46 (3) (1983), 301–333.

    Google Scholar 

  11. J. Taylor, Banach algebras and topology, Algebras in Analysis, ed. J.H. Williamson, Academic Press, 1975.

  12. V. Tolokonnikov, Stable rank ofH ∞ in multiply connected domains, Proc. Amer. Math. Soc. 117, (1993), 1023–1030.

    Google Scholar 

  13. S. Treil, Stable rank ofH ∞ is equal to one. J. Funct. Anal, 109 (1992), 130–154.

    Google Scholar 

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Authors and Affiliations

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

    Zongyao Wang & Yifeng Xue

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  1. Zongyao Wang
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  2. Yifeng Xue
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This project was supported by National Natural Science Foundation of China.

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Wang, Z., Xue, Y. On the unique finite (SI) decomposition of the Jordan operator ⊕ n i=1 S(θ) for certain inner function θ. Integr equ oper theory 36, 370–377 (2000). https://doi.org/10.1007/BF01213929

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  • DOI: https://doi.org/10.1007/BF01213929

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