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

Guemoula Asma, Abdelouahab Mansour


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.


Aluthge transformation, extended spectrum, Duggal transformation, self-adjoint operator, invertible operator

Subject classification

47A10, 47A25, 47A75, 47B49.


Laboratory of operator theory, Eloued University, Algeria

Full Text:



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

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

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

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

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

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)

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)

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

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

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)

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

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

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

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

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

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

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


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