Abstract
Motivated by recent investigations on norm-additive and spectrally multiplicative maps on various spaces of functions, in this paper we determine all bijective transformations between the positive cones of standard operator algebras over a Hilbert space which preserve a given symmetric norm of a given mean of elements. A result of similar spirit is also presented concerning transformations between cones of nonnegative elements of certain algebras of continuous functions.
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The authors were supported by the “Lendület” Program (LP2012-46/2012) of the Hungarian Academy of Sciences. The research was partially supported also by the European Union and the European Social Fund through project Supercomputer, the national virtual lab (grant no.: TAMOP-4.2.2.C-11/1/KONV-2012-0010).
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Molnár, L., Szokol, P. Transformations Preserving Norms of Means of Positive Operators and Nonnegative Functions. Integr. Equ. Oper. Theory 83, 271–290 (2015). https://doi.org/10.1007/s00020-015-2241-6
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DOI: https://doi.org/10.1007/s00020-015-2241-6