SZTE Bolyai Intézet - Simon Richárd: Preservers of the p-power and the Wasserstein means on 2x2 matrices

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Simon Richárd: Preservers of the p-power and the Wasserstein means on 2x2 matrices

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A leírásban a formázás megtartása (csak néhny naptár alkalmazás támogatja)

Kedd, 18. Április 2023, 10:30 - 23:45

In one of his recent papers L. Molnár, On dissimilarities of the conventional and Kubo-Ando power means in operator algebras, (J. Math. Anal. Appl., 504 (2021) 125356), Molnár showed that if

A

$\mathcal{A}$ is a von Neumann algebra without

I_{1}, I_{2}

$I_1, I_2$ -type direct summands, then any function from the positive definite cone of

A

$\mathcal{A}$ to the positive real numbers preserving the Kubo-Ando power mean, for some nonzero

p

$p$ between -1 and 1 is necessarily constant.
It was shown in that paper, that

I_{1}

$I_1$ -type algebras admit nontrivial

p

$p$ -power mean preserving functionals, and it was conjectured, that

I_{2}

$I_2$ -type algebras admit only constant

p

$p$ -power mean preserving functionals.
We confirm the latter. A similar result occured in L. Molnár, Maps on positive definite cones of

C^{*}

$C^*$ -algebras preserving the Wasserstein mean, Proc. Amer. Math. Soc. 150 (2022), 1209-1221., concerning the Wasserstein mean.
We prove the conjecture for

I_{2}

$I_2$ -type algebras in regard of the Wasserstein mean, too. We also give two conditions that characterise centrality in

C^{*}

$C^*$ -algebras.
Joint work with Dániel Virosztek.

The lecture will be in the Riesz lecture hall.

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Simon Richárd: Preservers of the p-power and the Wasserstein means on 2x2 matrices