106
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Spectra of the spherical Aluthge transform, the linear pencil, and a commuting pair of operators

, &
Pages 2533-2550 | Received 12 Mar 2020, Accepted 24 Jul 2020, Published online: 20 Aug 2020

References

  • Chavan S, Jabłoński ZJ, Jung IB, Stochel J. Taylor spectrum approach to Brownian-type operators with quasinormal entry (preprint 2020).
  • Du H-K, Pan J. Perturbation spectrum 2×2 operator matrices. Proc Amer Math Soc. 1994;121:761–766. doi: 10.1090/S0002-9939-1994-1185266-2
  • Kurbatova IV. Banach algebras associated with linear operator pencils. Math Notes. 2009;86:361–367. doi: 10.1134/S0001434609090090
  • Curto R, Yoon J. Aluthge transforms of 2-variable weighted shifts. Integral Equ Oper Theory. 2018;90. Art. 52, 32 pp. doi: 10.1007/s00020-018-2475-1
  • 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.
  • Taylor JL. A joint spectrum for several commuting operators. J Funct Anal. 1970;6:172–191. doi: 10.1016/0022-1236(70)90055-8
  • Curto R, Yoon J. Toral and spherical Aluthge transforms for 2-variable weighted shifts. C R Acad Sci Paris. 2016;354:1200–1204. doi: 10.1016/j.crma.2016.10.005
  • Curto R, Yoon J. Spherically quasinormal pairs of commuting operators. Analysis of operators on function space. Trends in Math. Basel: Birkhäuser/Springer; 2019. p. 213–237.
  • Curto R, Lee SH, Yoon J. Quasinormality of powers of commuting pairs of bounded operators. J Funct Anal. 2020;278(3):108342. 23 pp. doi: 10.1016/j.jfa.2019.108342
  • Kim J, Yoon J. Aluthge transforms and common invariant subspaces for a commuting n-tuple of operators. Integr Equ Oper Theory. 2017;87:245–262. doi: 10.1007/s00020-017-2343-4
  • Aluthge A. On p-hyponormal operators for 0<p<1. Integr Equ Oper Theory. 1990;13:307–315. doi: 10.1007/BF01199886
  • Curto R, Kim J, Yoon J. The Aluthge transform of unilateral weighted shifts and the Square Root Problem for finitely atomic measures. Math Nach. 2019;292:2352–2368. doi: 10.1002/mana.201800140
  • Ito M, Yamazaki T, Yanagida M. On the polar decomposition of the Aluthge transformation and related results. J Oper Theory. 2004;51:303–319.
  • Jung IB, Ko E, Pearcy C. Aluthge transform of operators. Integr Equ Oper Theory. 2000;37:437–448. doi: 10.1007/BF01192831
  • Lee SH, Yoon J. The square root problem and Aluthge transforms of weighted shifts. Math Nach. 2017;290:2925–2933. doi: 10.1002/mana.201600302
  • Yamazaki T. An expression of spectral radius via Aluthge transformation. Proc Amer Math Soc. 2002;130:1131–1137. doi: 10.1090/S0002-9939-01-06283-9
  • Kim HW, Kim J, Yoon J. Spherical Aluthge transform, spherical p and log-hyponormality of commuting pairs of operators. Linear Multilinear Algebra. Forthcoming.
  • Halmos PR. A Hilbert space problem book. Berlin and New York: Springer-Verlag; 1982.
  • Aiena P. Fredholm and local spectral theory, with applications to multipliers. Dordrecht: Kluwer Academic Publishers; 2004.
  • Cho M, Takaguchi M. Joint spectra of matrices. Sci Rep Hirosaki Univ. 1979;26:15–19.
  • Benhida C, Curto R, Lee SH, Yoon J. Joint spectra of spherical Aluthge transforms of commuting n-tuples of Hilbert space operators. C R Acad Sci Paris. 2019;357:799–802. doi: 10.1016/j.crma.2019.10.003
  • Horn RA, Johnson CR. Matrix analysis. Cambridge: Cambridge University Press; 1985.

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.