Abstract
In this work, we generalize the von Neumann and Davis theorems on the extension of the convexity of a group-invariant norm (resp. function) from the subspace of diagonal matrices to the whole space of complex (resp. hermitian) matrices. Our generalizations go in two directions: (1) We replace the space of complex (hermitian) matrices and its subspace of diagonal matrices by an Eaton triple and its subsystem. (2) We replace the Jensen (J) functional inducing the (usual) convexity of a function by the Hardy–Littlewood–Pólya–Karamata (HLPK) functional related to Wright-convexity and by the Sherman (S) functional connected with Sherman type convexity. The obtained results are interpreted for some classes of matrices.
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Niezgoda, M. Von Neumann–Davis type theorems for HLPK and Sherman functionals on Eaton triples. Period Math Hung 81, 46–64 (2020). https://doi.org/10.1007/s10998-020-00316-3
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DOI: https://doi.org/10.1007/s10998-020-00316-3