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- W2102014535 abstract "Let $mathcal{H}$ be an infinite dimensional Hilbert space, $mathcal{B}_{p}left(mathcal{H}right)$ the $p$-Schatten class of $mathcal{H}$ and $U_{p}left(mathcal{H}right)$ be the Banach-Lie group of unitary operators which are $p$-Schatten perturbations of the identity. Let $A$ be a bounded selfadjoint operator in $mathcal{H}$. We show that $$mathcal{O}_A:=left{UA : U in U_{p}left(mathcal{H}right) right}$$ is a smooth submanifold of the affine space $A + mathcal{B}_{p}left(mathcal{H}right)$ if only if $A$ has closed range. Furthermore, it is a homogeneous reductive space of $U_{p}left(mathcal{H}right)$. We introduce two metrics: one via the ambient Finsler metric induced as a submanifold of $A + mathcal{B}_{p}left(mathcal{H}right)$, the other, by means of the quotient Finsler metric provided by the homogeneous space structure. We show that $mathcal{O}_A$ is a complete metric space with the rectifiable distance of these metrics." @default.
- W2102014535 created "2016-06-24" @default.
- W2102014535 creator A5055430898 @default.
- W2102014535 date "2013-01-01" @default.
- W2102014535 modified "2023-09-27" @default.
- W2102014535 title "Geometry of the left action of the p-Schatten groups" @default.
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- W2102014535 doi "https://doi.org/10.15352/bjma/1358864549" @default.
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