Annals of Functional Analysis

On a conjecture of the norm Schwarz inequality

Tomohiro Hayashi

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Abstract

Let A be a positive invertible matrix, and let B be a normal matrix. Following the investigation of Ando, we show that A(BA1B)B, where denotes the geometric mean, fails in general.

Article information

Source
Ann. Funct. Anal., Volume 8, Number 3 (2017), 377-385.

Dates
Received: 6 October 2016
Accepted: 4 November 2016
First available in Project Euclid: 22 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1492826602

Digital Object Identifier
doi:10.1215/20088752-2017-0003

Mathematical Reviews number (MathSciNet)
MR3690000

Zentralblatt MATH identifier
1381.47009

Subjects
Primary: 47A63: Operator inequalities
Secondary: 47A64: Operator means, shorted operators, etc.

Keywords
operator theory operator mean geometric mean

Citation

Hayashi, Tomohiro. On a conjecture of the norm Schwarz inequality. Ann. Funct. Anal. 8 (2017), no. 3, 377--385. doi:10.1215/20088752-2017-0003. https://projecteuclid.org/euclid.afa/1492826602


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References

  • [1] T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26 (1979), 203–241.
  • [2] T. Ando, Geometric mean and norm Schwarz inequality, Ann. Funct. Anal. 7 (2016), no. 1, 1–8.
  • [3] R. Bhatia, Positive Definite Matrices, Princeton Ser. Appl. Math., Princeton Univ. Press, Princeton, NJ, 2007.
  • [4] S. Drury and M. Lin, private communications.