111
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Upper bounds for the Euclidean spectral radius of operators via joint norms

, & ORCID Icon
Pages 875-890 | Received 06 Apr 2023, Accepted 12 Nov 2023, Published online: 10 Jan 2024

References

  • Popescu G. Unitary invariants in multivariable operator theory. Mem Am Math Soc. 2009;200:vi+91 pp.
  • Bhunia P, Dragomir SS, Moslehian MS, et al. Lectures on numerical radius inequalities. Springer; 2022. (Infosys Science Foundation Series in Mathematical Sciences).
  • Feki K. Spectral radius of semi-Hilbertian space operators and its applications. Ann Funct Anal. 2020;11:929–946. doi: 10.1007/s43034-020-00064-y
  • Sunder VS. Functional analysis: spectral theory. Basel: Springer-Verlag; 1997.
  • Baklouti H, Feki K. On joint spectral radius of commuting operators in Hilbert spaces. Linear Algebra Appl. 2018;557:455–463. doi: 10.1016/j.laa.2018.08.017
  • Taylor JL. A joint spectrum for several commuting operators. J Funct Anal. 1970;6:172–191. doi: 10.1016/0022-1236(70)90055-8
  • Chō M, Takaguchi M. Boundary points of joint numerical ranges. Pac J Math. 1981;95:27–35. doi: 10.2140/pjm
  • Feki K, Yamazaki T. Joint numerical radius of spherical Aluthge transforms of tuples of Hilbert space operators. Math Inequal Appl. 2021;24(2):405–420.
  • Chavan S, Feki K. Spherical symmetry of some unitary invariants for commuting tuples. Oper Matrices. 2021;15(3):1131–1139. doi: 10.7153/oam-2021-15-70
  • Aluthge A. On p-hyponormal operators for 0<p<1. Integral Equ Oper Theory. 1990;13:307–315. doi: 10.1007/BF01199886
  • Antezana J, Pujals ER, Stojanoff D. The iterated Aluthge transforms of a matrix converge. Adv Math. 2011;226:1591–1620. doi: 10.1016/j.aim.2010.08.012
  • Chō M, Jung IB, Lee WY. On the iterated Duggal transform. Kyungpook Math J. 2009;49:647–650. doi: 10.5666/KMJ.2009.49.4.647
  • Dykema K, Schultz H. Brown measure and iterates of the Aluthge transform for some operators arising from measurable actions. Trans Am Math Soc. 2009;361:6583–6593. doi: 10.1090/S0002-9947-09-04762-X
  • Foiaş C, Jung I, Ko E, et al. Complete contractivity of maps associated with the Aluthge and Duggal transforms. Pac J Math. 2003;209:249–259. doi: 10.2140/pjm
  • Jung IB, Ko E, Pearcy C. Aluthge transform of operators. Integral Equ Oper Theory. 2000;37:437–448. doi: 10.1007/BF01192831
  • Jung IB, Ko E, Pearcy C. Spectral pictures of Aluthge transforms of operators. Integral Equ Oper Theory. 2001;40:52–60. doi: 10.1007/BF01202954
  • Yamazaki T. An expression of spectral radius via Aluthge transformation. Proc Am Math Soc. 2002;130:1131–1137. doi: 10.1090/proc/2002-130-04
  • Benhida C. Mind Duggal transforms. Filomat. 2019;33:5863–5870. doi: 10.2298/FIL1918863B
  • Chabbabi F. Product commuting maps with the λ-Aluthge transform. J Math Anal Appl. 2019;449:589–600. doi: 10.1016/j.jmaa.2016.12.027
  • Djordjević S, Kim J, Yoon J. Generalized spherical Aluthge transforms and binormality for commuting pairs of operators; preprint 2020.
  • Chō M, Tanahashi K. Spectral relations for Aluthge transform. Sci Math Jpn. 2002;55:77–83.
  • Kim J, Yoon J. Taylor spectra and common invariant subspaces through the Duggal and generalized Aluthge transforms for commuting n-tuples of operators. J Oper Theory. 2019;81:81–105. doi: 10.7900/jot
  • Benhida C, Curto RE, Lee SH, et al. Joint spectra of spherical Aluthge transforms of commuting d-tuples of Hilbert space operators. C R Math. 2019;357:799–802. doi: 10.1016/j.crma.2019.10.003
  • Curto R, Yoon J. Toral and spherical Aluthge transforms of 2-variable weighted shifts. C R Math. 2016;354:1200–1204. doi: 10.1016/j.crma.2016.10.005
  • Curto R, Yoon J. Aluthge transforms of 2-variable weighted shifts. Integral Equ Oper Theory. 2018;90:1–32. doi: 10.1007/s00020-018-2475-1
  • Curto R, Yoon J. Spherical Aluthge transforms and quasinormality for commuting pairs of operators. In: Aleman A, Hedenmalm H, Khavinson D, Putinar M, editors. Analysis of operators on function spaces (the Serguei Shimorin memorial volume), trends in mathematics. Cham: Birkhäuser; 2019. p. 213–237.
  • Kim J, Yoon J. Aluthge transforms and common invariant subspaces for a commuting n-tuple of operators. Integral Equ Oper Theory. 2017;87:245–262. doi: 10.1007/s00020-017-2343-4
  • Curto R, Lee SH, Yoon J. Quasinormality of powers of commuting pairs of bounded operators. J Funct Anal. 2020;278(3):108342. doi: 10.1016/j.jfa.2019.108342
  • Benhida C, Curto RE, Lee SH, et al. The spectral picture and joint spectral radius of the generalized spherical Aluthge transform. Adv Math. 2022;408(Part B):108602. doi: 10.1016/j.aim.2022.108602
  • Abu-Omar A, Kittaneh F. A numerical radius inequality involving the generalized Aluthge transform. Stud Math. 2013;216(1):69–75. doi: 10.4064/sm216-1-5

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.