115
Views
2
CrossRef citations to date
0
Altmetric
Research Article

C*-module operators which satisfy the generalized Cauchy–Schwarz type inequality

ORCID Icon
Pages 644-654 | Received 05 Jul 2022, Accepted 03 Nov 2022, Published online: 31 Dec 2022

References

  • Aldaz JM, Barza S, Fujii M, et al. Advances in operator Cauchy–Schwarz inequalities and their reverses. Ann Funct Anal. 2015;6(3):275–295.
  • Arambašić L, Bakić D, Moslehian MS. A treatment of the Cauchy–Schwarz inequality in C∗-modules. J Math Anal Appl. 2011;381:546–556.
  • Bhatia R, Davis C. A Cauchy–Schwartz inequality for operators with applications. Linear Algebra Appl. 1995;223-224:119–129.
  • Choi H, Kim Y, Ko E. On operators satisfying the generalized Cauchy–Schwarz inequality. Proc Am Math Soc. 2017;145:3447–3453.
  • Davis C. A Schwartz inequality for positive linear maps on C∗-algebras. Ill J Math. 1974;18:565–574.
  • Fang X, Moslehian MS, Xu Q. On majorization and range inclusion of operators on Hilbert C∗-modules. Linear Multilinear Algebra. 2018;66(12):2493–2500.
  • Fujii JI. Operator-valued inner product and operator inequalities. Banach J Math Anal. 2008;2(2):59–67.
  • Fujii JI, Fujii M, Seo Y. Operator inequalities on Hilbert C∗-modules via the Cauchy–Schwarz inequality. Math Inequal Appl. 2014;17(12):295–315.
  • Ilisević D, Varošanec S. On the Cauchy–Schwarz inequality and its reverse in semi-inner product C∗-modules. Banach J Math Anal. 2007;1(1):78–84.
  • Joiţa M. On the Cauchy–Schwarz inequality in C∗-algebras. Math Rep (Bucur). 2001;53(3): 243–246.
  • Kato T. Perturbation theory for linear operators. 2nd ed. Berlin Heidelberg, New York, Tokyo: Springer–Verlag; 1984.
  • Lance EC. Hilbert C∗-modules – a toolkit for operator algebraists. Cambridge: Cambridge University Press; 1995. (London Mathematical Society Lecture Note Series; vol. 210).
  • Liu N, Luo W, Xu Q. The polar decomposition for adjointable operators on Hilbert C∗-modules and centered operators. Adv Oper Theory. 2018;3(4):855–867.
  • Vosough M, Moslehian MS, Xu Q. Closed range and nonclosed range adjointable operators on Hilbert C∗-modules. Positivity. 2018;22:701–710.
  • Watanabe H. Operators characterized by certain Cauchy–Schwarz type inequalities. Publ Res Inst Math Sci. 1994;30(2):249–259.
  • Wegge-Olsen NE. K-theory and C-algebras: a friendly approach. Oxford: Oxford University Press; 1993.

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.