A Functional Analytic Perspective to the div-curl Lemma

We present an abstract functional analytic formulation of the celebrated \dive-\curl lemma found by F.~Murat and L.~Tartar. The viewpoint in this note relies on sequences for operators in Hilbert spaces. Hence, we draw the functional analytic relation of the div-curl lemma to differential forms and other sequences such as the \Grad\grad-sequence discovered recently by D.~Pauly and W.~Zulehner in connection with the biharmonic operator.Comment: 18 pages; some typos removed, Remark 2.3 added, Proposition 3.10 clarifie