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The trace as an average over the unit sphere of a normed space with a 1-symmetric basis
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The trace as an average over the unit sphere of a normed space with a 1-symmetric basis
classification
math.FA
math.CA
keywords
basismatrixnormedspheresymmetrictraceunitaverage
read the original abstract
We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis. Our result is new even in the case of $\ell_p$-norms in $\mathbb{R}^N$ for $p\neq 2$.
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