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On Semi-weakly n-Hyponormal Weighted Shifts

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Abstract

Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved that there exists a semi-weakly three-hyponormal weighted shift W α with α 0 = α 1 < α 2 which is not two-hyponormal, which illustrates the gaps between various weak subnormalities.

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Authors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, 702-701, Korea

    Younghae Do & Il Bong Jung

  2. Department of Mathematics, Bucknell University, Lewisburg, PA, 17837, USA

    George Exner

  3. Institute of System Science, Northeastern University, Shenyang, 110819, People’s Republic of China

    Chunji Li

Authors
  1. Younghae Do
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  2. George Exner
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  3. Il Bong Jung
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  4. Chunji Li
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Corresponding author

Correspondence to Il Bong Jung.

Additional information

Y. Do and I. B. Jung were supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. R01-2008-000-20088-0). C. Li was partially supported by the National Science Foundation of China (NSFC) under Grant 11171301.

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Do, Y., Exner, G., Jung, I.B. et al. On Semi-weakly n-Hyponormal Weighted Shifts. Integr. Equ. Oper. Theory 73, 93–106 (2012). https://doi.org/10.1007/s00020-012-1960-1

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  • DOI: https://doi.org/10.1007/s00020-012-1960-1

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