Abstract
We construct, for 1<p<∞,p ≠ 2, an operator onL pwhose distance to the space of compact operators onL pis not attained. We also show that the identity operator onL p,p ≠ 1,2, ∞ has a unique best compact approximation.
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Research partially supported by NSF grant DMS-8201635.
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Benyamini, Y., Lin, P.K. An operator onL pwithout best compact approximation. Israel J. Math. 51, 298–304 (1985). https://doi.org/10.1007/BF02764722
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DOI: https://doi.org/10.1007/BF02764722