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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the distance of subspaces of $ l\sp n\sb p$ to $ l\sp k\sb p$

Authors: William B. Johnson and Gideon Schechtman
Journal: Trans. Amer. Math. Soc. 324 (1991), 319-329
MSC: Primary 46B07
MathSciNet review: 989576
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Abstract: It is proved that if $ l_p^n$ is well-isomorphic to $ X \oplus Y$ and $ X$ either has small dimension or is a Euclidean space, then $ Y$ is well-isomorphic to $ l_p^k$, $ k = \operatorname{dim} Y$. The proofs use new forms of the finite dimensional decomposition method. It is shown that the constant of equivalence between a normalized $ K$-unconditional basic sequence in $ l_p^n$ and a subsequence of the unit vector basis of $ l_p^n$ is greatest, up to a constant depending on $ K$, when the sequence spans a $ 2$-Euclidean space.

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Keywords: Finite dimensional $ {L_p}$-spaces, complemented subspaces of $ {L_p}$, decomposition method, $ {\Lambda_p}$-sets
Article copyright: © Copyright 1991 American Mathematical Society