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Linear and Multilinear Algebra Volume 65, 2017 - Issue 11
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Articles

A sharp bound for the Frobenius norm of self-commutators of matrices

Michael Gil’Department of Mathematics, Ben Gurion University of the Negev, Beer-Sheva, Israel.Correspondence[email protected]
Pages 2333-2339 | Received 05 Feb 2016, Accepted 13 Oct 2016, Published online: 29 Dec 2016

References

  • Böttcher A, Wenzel D. How big can the commutator of two matrices be and how big is it typically? Linear Algebra Appl. 2005;403:216–228.
  • László L. Proof of Böttcher and Wenzel’s conjecture on commutator norms for 3-by-3 matrices. Linear Algebra Appl. 2007;422:659–663.
  • Vong S-W, Jin X-Q. Proof of Böttcher and Wenzel’s conjecture. Oper Matrices. 2008;2:435–442.
  • Böttcher A, Wenzel D. The Frobenius norm and the commutator. Linear Algebra Appl. 2008;429:1864–1885.
  • Wu Y-D, Liu X-Q. A short note on the Frobenius norm of the commutator. Math Notes. 2010;87(6):903–907.
  • Audenaert K. Variance bounds, with an application to norm bounds for commutators. Linear Algebra Appl. 2010;432:1126–1143.
  • Cheng C-M, Vong S-W, Wenzel D. Commutators with maximal Frobenius norm. Linear Algebra Appl. 2010;432:292–306.
  • Fong K-S, Cheng C-M, Lok I-K. Another unitarily invariant norm attaining the minimum norm bound for commutators. Linear Algebra Appl. 2010;433:1793–1797.
  • Wenzel D. Dominating the commutator. Oper Theory Adv Appl. 2010;202:579–600.
  • Gil’ MI. Operator functions and localization of spectra. Vol. 1830, Lecture notes in mathematics. Berlin: Springer-Verlag; 2003.
  • Gil’ MI. Bounds for eigenvalues of Schatten--von Neumann operators via selfcommutators. J Funct Anal. 2014;267(9):3500–3506.
  • Gil’ MI. Inequalities for eigenvalues of compact operators in a Hilbert space. Commun Contemp Math. 2016;18(1):1550022, 5p.
  • Dragomir SS. Some inequalities for commutators of bounded linear operators in a Hilbert space. Filomat. 2011;25(2):151–162.

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