Skip to main content
SpringerLink
Log in

Characterizations of a Complex Symmetric Truncated Backward Shift Type Operator Matrix and its Transforms

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper we study characterizations of a complex symmetric truncated shift type operator matrix and the Aluthge transform, the Duggal transform, the mean transform, and the generalized mean transform of such an operator matrix T (see (2.1) or (2.2)). As some applications of our main results, we give several examples of truncated shift type operator matrices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aluthge, A.: On \(p\)-hyponormal operators for \(0<p<\frac{1}{2}\). Int. Eq. Op. Th. 13, 307–315 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benhida, C.: Mind Duggal transform. Filomat 33(18), 5863–5870 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  3. Benhida, C., Chō, M., Ko, E., Lee, J.E.: On symmetric and skew-symmetric operators. Filomat 32(1), 293–303 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  4. Benhida, C., Chō, M., Ko, E., Lee, J.E.: On the generalized mean transform of complex symmetric operators. Banach J. Math. Anal. 14, 842–855 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chō, M., Lee, J.E., Motoyoshia, H.: On \([m, C]\)-Isometric Operators. Filomat 31(7), 2073–2080 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. Garcia, S.R.: Aluthge transform of complex symmetric operators. Int. Eq. Op. Th. 60, 357–367 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Garcia, S.R., Lutz, B., Timotin, D.: Two remarks about nilpotent operators of order two. Proc. Am. Math. Soc. 142(5), 1749–1756 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Garcia, S.R., Putinar, M.: Complex symmetric operators and applications. Trans. Am. Math. Soc. 358, 1285–1315 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Garcia, S.R., Putinar, M.: Complex symmetric operators and applications II. Trans. Am. Math. Soc. 359, 3913–3931 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Garcia, S.R., Wogen, W.R.: Some new classes of complex symmetric operators. Trans. Amer. Math. Soc. 362, 6065–6077 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Garcia, S.R., Complex, W.R.: symmetric partial isometries. J. Funct. Anal. 257, 1251–1260 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Guyker, J.: A structure theorem for operators with closed range. Bull. Austral. Math. Soc. 18, 169–186 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  13. Halmos, P.R., Wallen, L.J.: Powers of partial isometries, J. Math. Mech. 19, 657–663, (1969/1970)

  14. Jung, I., Ko, E., Pearcy, C.: Aluthge transform of operators. Int. Eq. Op. Th. 37, 437–448 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Jung, I., Ko, E., Pearcy, C.: The iterated Aluthge transform of an operator. Int. Eq. Op. Th. 45, 375–387 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Jung, I., Ko, E., Pearcy, C.: Completely contractivity of maps associated with Aluthge and Duggal transforms. Pacific J. Math. 209(2), 249–259 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Jung, S., Ko, E., Lee, M., Lee, J.E.: On local spectral properties of complex symmetric operators. J. Math. Anal. Appl. 379, 325–333 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jung, S., Ko, E., Lee, J.E.: On scalar extensions and spectral decompositions of complex symmetric operators. J. Math. Anal. Appl. 382, 252–260 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lee, S., Lee, W., Yoon, J.: The mean transform of bounded linear operators. J. Math. Anal. Appl. 410, 70–81 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lambert, A.: Unitary equivalence and reducibility of invertible weighted shifts. Bull Austral. Math. Soc. 5, 157–173 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhu, S., Li, C.G.: Complex symmetric weighted shift. Trans. Am. Math. Soc. 365(1), 511–530 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Shields, A.L.: Weighted shift operators and analytic function theory. Math. Surv. Am. Math. Soc. Providence RI 13, 49–128 (1974)

    MathSciNet  MATH  Google Scholar 

  23. Wang, X., Gao, Z.: A note on Aluthge transforms of complex symmetric operators and applications. Int. Eq. Op. Th. 65, 573–580 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Author notes

  1. In honor of the 70th birthday of Professor Muneo Chō.

Authors and Affiliations

  1. Laboratoire Paul Painlevé, Université de Lille, 59655, Villeneuve Cedex, France

    Chafiq Benhida

  2. Kanagawa University, 15-3-1113, Tsutsui-machi Yahatanishi-ku, Kita-kyushu, 806-0032, Japan

    Muneo Chō

  3. Department of Mathematics, Ewha Womans University, Seoul, 120-750, Korea

    Eungil Ko

  4. Department of Mathematics and Statistics, Sejong University, Seoul, 05006, Korea

    Ji Eun Lee

Authors
  1. Chafiq Benhida
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muneo Chō
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eungil Ko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ji Eun Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

These authors contributed equally to this work. The first named author was partially supported by Labex CEMPI (ANR-11-LABX-0007-01). The second author is partially supported by Grant-in-Aid Scientific Research No. 15K04910. The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058633). The fourth author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (No. 2022R1H1A2091052).

Corresponding author

Correspondence to Ji Eun Lee.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Benhida, C., Chō, M., Ko, E. et al. Characterizations of a Complex Symmetric Truncated Backward Shift Type Operator Matrix and its Transforms. Results Math 78, 13 (2023). https://doi.org/10.1007/s00025-022-01786-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00025-022-01786-2

Keywords

Mathematics Subject Classification

Search

Navigation