Extensions of Bernstein’s Lethargy Theorem

  • Asuman Güven AksoyEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 264)


In this paper, we examine the aptly-named “Lethargy Theorem” of Bernstein and survey its recent extensions. We show that one of these extensions shrinks the interval for best approximation by half while the other gives a surprising connection to the space of bounded linear operators between two Banach spaces.


Best approximation Bernstein’s Lethargy theorem Approximation numbers 

Mathematics Subject Classification (2000)

41A25 41A50 46B20 


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Authors and Affiliations

  1. 1.Department of Mathematical SciencesClaremont McKenna CollegeClaremontUSA

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