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- W4387432593 abstract "Given two Hermitian matrices, $A$ and $B$, we introduce a new type of spectral measure, a $textit{tracial joint spectral measure}$ $mu_{A, B}$ on the plane. Existence of this measure implies the following two results: 1) any two-dimensional subspace of the Schatten-$p$ class is isometric to a subspace of $L_{p}$, and 2) if $f : mathbb{R} to mathbb{R}$ has non-negative $k$th derivative and $A$ and $B$ are Hermitian matrices with $A$ positive semidefinite, then $t mapsto mathrm{tr}~f(t A + B)$ has non-negative $k$th derivative. We also give an explicit expression for the measure $mu_{A, B}$." @default.
- W4387432593 created "2023-10-09" @default.
- W4387432593 creator A5068891970 @default.
- W4387432593 date "2023-10-04" @default.
- W4387432593 modified "2023-10-09" @default.
- W4387432593 title "Tracial joint spectral measures" @default.
- W4387432593 doi "https://doi.org/10.48550/arxiv.2310.03227" @default.
- W4387432593 hasPublicationYear "2023" @default.
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