Fréchet differentiability of the norm of $L_p$-spaces associated with arbitrary von Neumann algebras
Denis PotapovSchool of Mathematics and Statistics, University of New South Wales, Kensington, New South Wales 2052, AustraliaFedor SukochevSchool of Mathematics and Statistics, University of New South Wales, Kensington, New South Wales 2052, AustraliaAnna TomskovaSchool of Mathematics and Statistics, University of New South Wales, Kensington, New South Wales 2052, AustraliaD. ZaninSchool of Mathematics and Statistics, University of New South Wales, Kensington, New South Wales 2052, Australia
2017en
ABI
Аннотация
Let $\mathcal M$ be a von Neumann algebra, and let $({\mathcal {L}}_p(\mathcal M),\|\cdot \|_p)$, $1\le p<\infty$ be the Haagerup $L_p$-space on $\mathcal M$. We prove that the differentiability properties of $\|\cdot \|_p$ are precisely the same as those of classical (commutative) $L_p$-spaces. Our main instruments are the theories of multiple operator integrals and singular traces.
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