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Conditions Implying Self-adjointness of Operators

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Abstract.

In this paper, we show that if \(T \in {\mathcal{B}}({\mathcal{H}})\) is a quasi-class A operator and S is an arbitrary operator for which \(0 \notin \overline{W(S)}\) and ST = T*S, then T is self-adjoint, and we also show that quasisimilar quasi-class A operators have equal spectra and essential spectra.

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Authors and Affiliations

  1. Department of Mathematics Education, Seoul National University of Education, Seoul, 137-742, Korea

    In Ho Jeon

  2. Department of Mathematics, University of Incheon, Incheon, 402-749, Korea

    In Hyoun Kim

  3. Department of Mathematics, Tohoku Pharmaceutical University, Sendai, 981-8558, Japan

    Kotaro Tanahashi

  4. Department of Mathematics, Sendai National College of Technology, Sendai, 989-3124, Japan

    Atsushi Uchiyama

Authors
  1. In Ho Jeon
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  2. In Hyoun Kim
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  3. Kotaro Tanahashi
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  4. Atsushi Uchiyama
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Corresponding author

Correspondence to In Hyoun Kim.

Additional information

This work of the second author was supported by the University of Incheon Research Grant in 2008.

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Jeon, I.H., Kim, I.H., Tanahashi, K. et al. Conditions Implying Self-adjointness of Operators. Integr. equ. oper. theory 61, 549–557 (2008). https://doi.org/10.1007/s00020-008-1598-1

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  • DOI: https://doi.org/10.1007/s00020-008-1598-1

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