Korean J. Math. Vol. 29 No. 3 (2021) pp.511-518
DOI: https://doi.org/10.11568/kjm.2021.29.3.511

Extended spectrum of the Aluthge transformation

Article Sidebar

PDF
Published: Aug 25, 2021
Keywords:
Aluthge transformation, extended spectrum, Duggal transformation, self-adjoint operator, invertible operator
Mathematics Subject Classification:
47A10, 47A25, 47A75, 47B49.

Main Article Content

Guemoula Asma
Department of Mathematics, Operators Theory and PDE Foundations and Applications Laboratory, University of El-Oued, P. O. Box 789, El-Oued 39000, Algeria.
Abdelouahab Mansour
Department of Mathematics, Operators Theory and PDE Foundations and Applications Laboratory, University of El-Oued, P. O. Box 789, El-Oued 39000, Algeria.

Abstract

In this paper, a relationship between the extended spectrum of the Aluthge transform and the extended spectrum of the operator $T$ is proved. Other relationships between two different operators and other results are also given.



Article Details

Supporting Agencies

Laboratory of operator theory Eloued University Algeria

References

[1] H. Alkanjo; On extended eigenvalues and extended eigenvectors of truncated shift, Concrete Operators 1(2013), 19–27. Google Scholar

[2] A. Aluthge; On p-hyponormal Operators for 0 < p < 1, Integral Equations Operator Theory 13(1990), 307–315. Google Scholar

[3] A. Biswas, A. Lambert, and S. Petrovic; Extended eigenvalues and the Volterra operator, Glasg. Math. J., 44(3) (2002), 521–534. Google Scholar

[4] A. Biswas, S. Petrovic; On extended eigenvalues of operators, Integral Equations Operator Theory, 55(2) (2006), 233–248. Google Scholar

[5] G. Cassier, H. Alkanjo; Extended spectrum, extended eigenspaces and normal operators, J. Math. Anal. Appl, 418(1) (2014), 305–316. Google Scholar

[6] K. Dykema, H. Schultz; Brown measure and iterates of the Aluthge transform for some operators arising from measurable actions, Trans. Amer. Math. Soc. 361(2009), 6583–6593. Google Scholar

[7] C. Foias, I. B. Jung, E. Ko and C. Pearcy; Complete Contractivity of Maps Associated with the Aluthge and Duggal Transform, s, Pacific J. Math. 209 (2003), 249-259. Google Scholar

[8] T. Furuta; Invitation to linear operators, Taylor and Fran. Loondon, (2001). Google Scholar

[9] T. Huruya; A note on p-hyponormaI operators, Proc. Amer. Math. Soc. 125 (1997), 3617-3624. Google Scholar

[10] M. Ito, T. Yamazaki and M. Yanagida; On the polar decomposition of the Aluthge transformation and related results, J. Operator Theory 51(2004), 303–319. Google Scholar

[11] I. Jung, E. Ko, and C. Pearcy; Aluthge transforms of operators, Integral Equations Operator Theory 37 (2000),437-448. Google Scholar

[12] K. Okuba; on weakly unitarily invariant norm and the Aluthge transformation, Linear Algebra Appl, 371 (2003), 369-375. Google Scholar

[13] M. Sertbas, F. Yilmaz; On the extended spectrumof some quasinormal operators, Turk. J. Math, 41 (2017), 1477–1481. Google Scholar

[14] T.Y. Tam; -Aluthge iteration and spectral radius, Integral Equations Operator Theory 60(2008), 591–596. Google Scholar

[15] T. Yamazaki; An expression of spectral radius via Aluthge transformation, Proc. Amer. Math. Soc. 130(2002), 1131–1137. Google Scholar

[16] T. Yamazaki; On numerical range of the Aluthge transformation, Linear Algebra Appl. 341 (2002), 111-117. Google Scholar

[17] K. Zaiz, A. Mansour; On numerical range and numerical radius of convex function operators , Korean J. Math. 27 (2019), 879-898. Google Scholar