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Minimal rank and reflexivity of operator spaces

Authors:	Roy Meshulam Peter Semrl

Institution:	Department of Mathematics, Technion, Haifa 32000, Israel ; Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

Abstract:	Let ${\mathcal{S}}$ be an -dimensional space of linear operators between the linear spaces and over an algebraically closed field $\mathbb{F}$ . Improving results of Larson, Ding, and Li and Pan we show the following. Theorem. Let $S_1, \ldots , S_n$ be a basis of $\mathcal{S}$ . Assume that every nonzero operator in $\mathcal{S}$ has rank larger than . Then a linear operator $T : U \to V$ belongs to $\mathcal{S}$ if and only if for every $u\in U$ , is a linear combination of $S_1 u , \ldots , S_n u$ .

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