High Quality Content by WIKIPEDIA articles! In mathematics, Schur's property, named after Issai Schur, is the property of normed spaces that is satisfied precisely if weak convergence of sequences entails convergence in norm.When we are working in a normed space X and we have a sequence (xn) that converges weakly to x (see weak convergence), then a natural question arises. Does the sequence converge in perhaps a more desirable manner? That is, does the sequence converge to x in norm?This property was named after the early 20th century mathematician Issai Schur who showed that l1 had the above property in his 1921 paper.

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