We construct a quasi-Banach function lattice $X$ on $\mathbb R$ whose quasi-norm is order continuous and invariant under every translation. Nevertheless, $X$ contains a bounded sequence with common compact support which is equicontinuous in $X$ and has no norm-convergent subsequence. This provides a counterexample to C...
Under mild assumptions, the main results of this paper characterize a (real or complex) symmetric operator space affiliated with a semi-finite atomless von Neumann algebra $(\mathcal M, \tau)$ possessing the Daugavet property as $L_1(\mathcal M,\tau)$ or $\mathcal M$ (up to equivalent norms, or even proportional norms)...
Jing-Hao Huang, Yerlan Nessipbayev, F. Sukochev et al.· 1 citation
Let $\mathcal{M}$ be a factor equipped with a semi-finite faithful normal trace $\tau$. Let $E(0,\infty)$ be a symmetrically normed function space and $E(\mathcal{M},\tau)$ be the corresponding symmetrically normed operator space. Suppose that $a, b$ are $\tau$-measurable operators affiliated with $\mathcal{M}$. It is...
Jing-Hao Huang, F. Sukochev, Ran Xu et al.· 0 citations
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