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Algebraic extensions of semi-hyponormal operators

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Abstract

In this paper, we show that algebraic extensions of semi-hyponormal operators (defined below) are subscalar. As corollaries we get the following:

  1. (1)

    Everyk-quasihyponormal operator is subscalar.

  2. (2)

    Every algebraic extension of Aluthge transforms ofp-hyponormal operators is subscalar.

From these results and [Es] it is known that such operators with ‘rich spectra’ have nontrivial invariant subspaces.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, 440-746, Suwon, Korea

    Mee-Kyoung Kim

  2. Department of Mathematics, Ewha Women's University, 120-750, Seoul, Korea

    Eungil Ko

Authors
  1. Mee-Kyoung Kim
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  2. Eungil Ko
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The second author was supported by the grant for the promotion of scientic research in women's universities.

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Kim, MK., Ko, E. Algebraic extensions of semi-hyponormal operators. Integr equ oper theory 37, 449–456 (2000). https://doi.org/10.1007/BF01192832

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  • DOI: https://doi.org/10.1007/BF01192832

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