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Maps Preserving Schatten Norms of Power Means of Positive Operators

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Abstract

In this paper, we determine the general form of transformations on positive operators preserving a p-norm of a power mean with positive exponent. The corresponding theorems complement a former result of ours, in which we did the same concerning the operator norm and the cone of invertible positive operators on a finite dimensional complex Hilbert space.

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References

  1. Carlen, E.: Trace inequalities and quantum entropy: an introductory course. Contemp. Math. 529, 73–140 (2010)

    Article  MathSciNet  Google Scholar 

  2. Gaál, M.: Maps on quantum states in \(C^*\)-algebras preserving von Neumann entropy or Schatten \(p\)-norm of convex combinations. Can. Math. Bull. https://doi.org/10.4153/CMB-2018-011-3

  3. Gaál, M.: Norm-additive maps on the positive definite cone of a \(C^{*}\)-algebra (submitted)

  4. Gaál, M., Nagy, G.: Preserver problems related to quasi-arithmetic means of invertible positive operators. Integr. Equ. Oper. Theory 90, 7 (2018)

    Article  MathSciNet  Google Scholar 

  5. Gaál, M., Nagy, G.: Maps on Hilbert space effect algebras preserving norms of operator means. Acta Sci. Math. (Szeged) 84, 201–208 (2018)

    Article  MathSciNet  Google Scholar 

  6. Gaál, M., Nagy, G.: A characterization of unitary-antiunitary similarity transformations via Kubo-Ando means. Anal. Math. (in press)

  7. Gehér, G.P.: An elementary proof for the non-bijective version of Wigner’s theorem. Phys. Lett. A 378, 2054–2057 (2014)

    Article  MathSciNet  Google Scholar 

  8. Hiai, F., Petz, D.: Introduction to Matrix Analysis and Applications. Springer, Berlin (2014)

    Book  Google Scholar 

  9. Kuo, D.L.-W., Tsai, M.-C., Wong, N.-C., Zhang, J.: Maps preserving Schatten \(p\)-norms of convex combinations. Abstr. Appl. Anal. 2014, 520795 (2014)

    Google Scholar 

  10. McCarthy, C.A.: \(c_p\). Israel J. Math. 5, 249–271 (1967)

    Google Scholar 

  11. Molnár, L.: Order automorphisms on positive definite operators and a few applications. Linear Algebra Appl. 434, 2158–2169 (2011)

    Article  MathSciNet  Google Scholar 

  12. Molnár, L., Szokol, P.: Transformations preserving norms of means of positive operators and nonnegative functions. Integr. Equ. Oper. Theory 83, 271–290 (2015)

    Article  MathSciNet  Google Scholar 

  13. Nagy, G.: Preservers for the p-norm of linear combinations of positive operators. Abstr. Appl. Anal. 2014, 434121 (2014)

    Article  MathSciNet  Google Scholar 

  14. Szokol, P., Tsai, M.C., Zhang, J.: Preserving problems of geodesic-affine maps and related topics on positive definite matrices. Linear Algebra Appl. 483, 293–308 (2015)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The author was supported by the National Research, Development and Innovation Office NKFIH Reg. No. K115383.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, P.O. Box 400, Debrecen, 4002, Hungary

    Gergő Nagy

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  1. Gergő Nagy
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Correspondence to Gergő Nagy.

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Nagy, G. Maps Preserving Schatten Norms of Power Means of Positive Operators. Integr. Equ. Oper. Theory 90, 59 (2018). https://doi.org/10.1007/s00020-018-2487-x

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  • DOI: https://doi.org/10.1007/s00020-018-2487-x

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