Geodesic
Completeness of symmetric $\varDelta $-normed spaces of $\tau $-measurable operators
Jinghao Huang1 ; Galina Levitina2 ; Fedor Sukochev2
1Department of Mathematics Sun Yat-Sen University Guangzhou, 510275, P.R. China Current address: School of Mathematics and Statistics University of New South Wales Kensington, NSW 2052, Australia
2School of Mathematics and Statistics University of New South Wales Kensington, NSW 2052, Australia
Studia Mathematica, Tome 237 (2017) no. 3, pp. 201-219
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Let ${\mathcal M}$ be an arbitrary semifinite von Neumann algebra equipped with a faithful normal semifinite trace $\tau $ and let $E$ be a complete symmetric $\varDelta $-normed function space. We show that the corresponding symmetric space $E({\mathcal M},\tau )$ of $\tau $-measurable operators in $S({\mathcal M},\tau )$ is a complete symmetrically $\varDelta $-normed ideal.
DOI : 10.4064/sm8349-10-2016
Keywords: mathcal arbitrary semifinite von neumann algebra equipped faithful normal semifinite trace tau complete symmetric vardelta normed function space corresponding symmetric space mathcal tau tau measurable operators mathcal tau complete symmetrically vardelta normed ideal

Jinghao Huang  1   ; Galina Levitina  2   ; Fedor Sukochev  2

1 Department of Mathematics Sun Yat-Sen University Guangzhou, 510275, P.R. China Current address: School of Mathematics and Statistics University of New South Wales Kensington, NSW 2052, Australia
2 School of Mathematics and Statistics University of New South Wales Kensington, NSW 2052, Australia 
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Jinghao Huang; Galina Levitina; Fedor Sukochev. Completeness of symmetric $\varDelta $-normed spaces of $\tau $-measurable operators. Studia Mathematica, Tome 237 (2017) no. 3, pp. 201-219. doi: 10.4064/sm8349-10-2016

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