𝐿𝑈-factorization of operators on 𝑙₁

Andrews, Kevin T.; Smith, Philip W.; Ward, Joseph D.

doi:10.1090/S0002-9939-1986-0854027-9

$LU$-factorization of operators on $l_ 1$
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by Kevin T. Andrews, Philip W. Smith and Joseph D. Ward

Proc. Amer. Math. Soc. 98 (1986), 247-252

DOI: https://doi.org/10.1090/S0002-9939-1986-0854027-9

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Abstract:

Necessary and sufficent conditions are obtained for LU-factorization of operators on ${l_1}$. In particular it is shown that uniform invertibility of the compressions of the operator is not sufficient to insure an LU-factorization of the operator, thus answering a question of de Boor, Jia, and Pinkus.

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