{"paper":{"title":"Two-sided multiplication operators on the space of regular operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anton R. Schep, Jin Xi Chen","submitted_at":"2016-09-22T11:14:17Z","abstract_excerpt":"Let $W$, $X$, $Y$ and $Z$ be Dedekind complete Riesz spaces. For $A\\in L^{r}(Y, Z)$ and $B\\in L^{r}(W, X)$ let $M_{A,\\,B}$ be the two-sided multiplication operator from $L^{r}(X, Y)$ into $L^r(W,\\,Z)$ defined by $M_{A,\\,B}(T)=ATB$. We show that for every $0\\leq A_0\\in L^{r}_{n}(Y, Z)$, $|M_{A_0, B}|(T)=M_{A_0, |B|}(T)$ holds for all $B\\in L^{r}(W, X)$ and all $T\\in L^{r}_{n}(X, Y)$. Furthermore, if $W$, $X$, $Y$ and $Z$ are Dedekind complete Banach lattices such that $X$ and $Y$ have order continuous norms, then $|M_{A,\\, B}|=M_{|A|, \\,|B|}$ for all $ A\\in L^{r}(Y, Z)$ and all $B\\in L^{r}(W, X"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06913","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}